| Preface |
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vii | |
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1 | (8) |
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9 | (104) |
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Contraction Mapping Principle in Uniform Topological Spaces and Applications |
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9 | (1) |
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Banach Contraction Mapping Principle in Uniform Spaces |
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10 | (17) |
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14 | (13) |
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Further Generalization of Banach Contrction Mapping Principle |
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27 | (7) |
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Fixed Point Theorems for Some Extension of Contraction Mappings on Uniform Spaces |
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28 | (4) |
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An Interplay Between the Order and Pseudometric Partial Ordering in Complete Uniform Topological Space |
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32 | (2) |
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34 | (10) |
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38 | (5) |
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On the Approximate Iteration |
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43 | (1) |
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The Contraction Mapping Principle Applied to the Cauchy-Kowalevsky Theorem |
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44 | (9) |
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45 | (1) |
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46 | (4) |
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50 | (3) |
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An Implicit Function Theorem for a Set of Mappings and Its Application to Nonlinear Hyperbolic Boundary Value Problem as Application of Contraction Mapping Principle |
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53 | (30) |
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An Implicit Function Theorem for a Set of Mappings |
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55 | (5) |
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Notations and Preliminaries |
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60 | (1) |
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Results of Smiley on Linear Problem |
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61 | (5) |
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Alternative Problem and Approximate Equations |
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66 | (7) |
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Application to Nonlinear Wave Equations --- A Theorem of Paul Rabinowitz |
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73 | (10) |
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83 | (8) |
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88 | (3) |
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Iterated Function Systems (IFS) and Attractor |
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91 | (12) |
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94 | (9) |
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103 | (4) |
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104 | (1) |
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105 | (1) |
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106 | (1) |
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Random Fixed Point and Set-Valued Random Contraction |
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107 | (6) |
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Some Fixed Point Theorems in Partially Ordered Sets |
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113 | (38) |
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Fixed Point Theorems and Applications to Economics |
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113 | (1) |
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Fixed Point Theorem on Partially Ordered Sets |
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113 | (3) |
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Applications to Games and Economics |
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116 | (9) |
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117 | (1) |
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118 | (1) |
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119 | (1) |
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The Contraction Mapping Principle in Uniform Space via Kleene's Fixed Point Theorem |
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120 | (4) |
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Applications on Double Ranked Sequence |
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124 | (1) |
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Lattice Theoretical Fixed Point Theorems of Tarski |
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125 | (6) |
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Applications of Lattice Fixed Point Theorem of Tarski to Integral Equations |
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131 | (3) |
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The Tarski-Kantorovitch Principle |
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134 | (2) |
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The Iterated Function Systems on (2x,⊃) |
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136 | (3) |
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The Iterated Function Systems on (C(X),⊃) |
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139 | (2) |
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The Iterated Function System on (K(X),⊃) |
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141 | (1) |
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Continuity of Maps on Countably Compact and Sequential Spaces |
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142 | (4) |
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Solutions of Impulsive Differential Equations |
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146 | (5) |
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147 | (2) |
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149 | (2) |
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Topological Fixed Point Theorems |
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151 | (114) |
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Brouwer Fixed Point Theorem |
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151 | (20) |
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160 | (2) |
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Fixed Point Theorems of Set Valued Mappings with Applications in Abstract Economy |
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162 | (5) |
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167 | (2) |
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Equilibrium Point of Abstract Economy |
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169 | (2) |
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Fixed Point Theorems and KKM Theorems |
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171 | (6) |
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Duality in Fixed Point Theory of Set Valued Mappings |
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174 | (3) |
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Applications on Minimax Principles |
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177 | (5) |
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Applications on Sets with Convex Sections |
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179 | (3) |
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More on Sets with Convex Sections |
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182 | (8) |
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More on the Extension of KKM Theorem and Ky Fan's Minimax Principle |
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190 | (5) |
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A Fixed Point Theorem Equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz Theorem |
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195 | (5) |
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More on Fixed Point Theorems |
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200 | (6) |
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Applications of Fixed Point Theorems to Equilibrium Analysis in Mathematical Economics and Game Theory |
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206 | (18) |
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Fixed Point and Equilibrium Point |
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207 | (4) |
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Existence of Maximal Elements |
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211 | (2) |
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Equilibrium Existence Theorems |
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213 | (11) |
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Fixed Point of ψ-Condensing Mapping, Maximal Elements and Equilibria |
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224 | (20) |
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Equilibrium on Paracompact Spaces |
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237 | (3) |
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Equilibria of Generalized Games |
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240 | (3) |
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243 | (1) |
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Coincidence Points and Related Results, an Analysis on H-Spaces |
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244 | (17) |
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Applications to Mathematical Economics: An Analogue of Debreu's Social Equilibrium Existence Theorem |
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261 | (4) |
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Variational and Quasivariational Inequalities in Topological Vector Spaces and Generalized Games |
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265 | (182) |
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Simultaneous Variational Inequalities |
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265 | (19) |
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Variational Inequalities for Single Valued Functions |
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265 | (3) |
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Solutions of Simultaneous Nonlinear Variational Inequalities |
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268 | (8) |
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Application to Nonlinear Boundary Value Problem for Quasilinear Operator of Order 2m in Generalized Divergence Form |
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276 | (4) |
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Minimization Problems and Related Results |
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280 | (2) |
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Extension of a Karamardian Theorem |
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282 | (2) |
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Variational Inequalities for Setvalued Mappings |
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284 | (17) |
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Simultaneous Variational Inequalities |
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287 | (5) |
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Implicit Variational Inequalities --- The Monotone Case |
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292 | (4) |
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Implicit Variational Inequalities --- The USC Case |
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296 | (5) |
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Variational Inequalities and Applications |
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301 | (5) |
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Application to Minimization Problems |
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304 | (2) |
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Duality in Variational Inequalities |
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306 | (6) |
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309 | (3) |
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A Variational Inequality in Non-Compact Sets with Some Applications |
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312 | (9) |
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Browder-Hartman-Stampacchia Variational Inequalities for Set-Valued Monotone Operators |
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321 | (4) |
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321 | (1) |
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An Existence Theorem of Variational Inequalities |
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322 | (3) |
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Some Generalized Variational Inequalities with Their Applications |
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325 | (10) |
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Some Generalized Variational Inequalities |
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325 | (8) |
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Applications to Minimization Problems |
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333 | (2) |
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Some Results of Tarafdar and Yuan on Generalized Variational Inequalities in Locally Convex Topological Vector Spaces |
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335 | (5) |
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Some Generalized Variational Inequalities |
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337 | (3) |
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Generalized Variational Inequalities for Quasi-Monotone and Quasi-Semi-Monotone Operators |
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340 | (23) |
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Generalization of Ky Fan's Minimax Inequality |
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346 | (2) |
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Generalized Variational Inequalities |
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348 | (10) |
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358 | (5) |
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Generalization of Ky Fan's Minimax Inequality with Applications to Generalized Variational Inequalities for Pseudo-Monotone Type I Operators and Fixed Point Theorems |
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363 | (16) |
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Generalization of Ky Fan's Minimax Inequality |
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365 | (7) |
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Generalized Variational Inequalities |
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372 | (5) |
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Applications to Fixed Point Theorems |
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377 | (2) |
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Generalized Variational-Like Inequalities for Pseudo-Monotone Type I Operators |
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379 | (9) |
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Existence Theorems for GV LI (T, mu, h, X, F) |
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383 | (5) |
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Generalized Quasi-Variational Inequalities |
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388 | (9) |
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Generalized Quasi-Variational Inequalities for Monotone and Lower Semi-Continuous Mappings |
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388 | (5) |
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Generalized Quasi-Variational Inequalities for Upper Semi-Continuous Mappings Without Monotonicity |
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393 | (4) |
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Generalized Quasi-Variational Inequalities for Lower and Upper Hemi-Continuous Operators on Non-Compact Sets |
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397 | (12) |
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Generalized Quasi-Variational Inequalities for Lower Hemi-Continuous Operators |
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398 | (6) |
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Generalized Quasi-Variational Inequalities for Upper Hemi-Continuous Operators |
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404 | (5) |
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Generalized Quasi-Variational Inequalities for Upper Semi-Continuous Operators on Non-Compact Sets |
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409 | (6) |
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Non-Compact Generalized Quasi-Variational Inequalities |
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410 | (5) |
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Generalized Quasi-Variational Inequalities for Pseudo-Monotone Set-Valued Mappings |
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415 | (11) |
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Generalized Quasi-Variational Inequalities for Strong Pseudo-Monotone Operators |
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415 | (6) |
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Generalized Quasi-Variational Inequalities for Pseudo-Monotone Set-Valued Mappings |
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421 | (5) |
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Non-Linear Variational Inequalities and the Existence of Equilibrium in Economics with a Riesz Space of Commodities |
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426 | (4) |
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Existence of Equilibrium Lemma |
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428 | (2) |
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Equilibria of Non-compact Generalized Games with L* Majorized Preference Correspondences |
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430 | (8) |
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Existence of Maximal Elements |
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430 | (4) |
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Existence of Equilibrium for Non-Compact Abstract Economies |
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434 | (4) |
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Equilibria of Non-compact Generlized Games |
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438 | (9) |
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Equilibria of Generalized Games |
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442 | (3) |
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Tarafdar and Yuan's Application on Existence Theorem of Equilibria for Constrained Games |
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445 | (2) |
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Best Approximation and Fixed Point Theorems for Set-Valued Mappings in Topological Vector Spaces |
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447 | (16) |
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448 | (4) |
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452 | (11) |
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Some Lemmas and Relevant Results |
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454 | (9) |
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Degree Theories for Set-Valued Mappings |
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463 | (100) |
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Degree Theory for Set-Valued Ultimately Compact Vector Fields |
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463 | (8) |
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Properties of the Degree of Ultimately Compact Vector Fields |
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465 | (2) |
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k-ø-Contractive Set Valued Mappings |
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467 | (4) |
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Coincidence Degree for Non-Linear Single-Valued Perturbations of Linear Fredholm Mappings |
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471 | (7) |
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473 | (1) |
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Definition of Coincidence Degree |
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474 | (1) |
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Properties of the Coincidence Degree |
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475 | (3) |
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On the Existence of Solutions of the Equation Lx ε Nx and a Coincidence Degree Theory |
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478 | (19) |
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Coincidence Degree for Set-Valued k --- ø-Contractive Perturbations of Linear Fredholm Mappings |
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479 | (18) |
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Coincidence Degree for Multi-Valued Mappings with Non-Negative Index |
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497 | (10) |
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Basic Assumptions and Main Results in Akashi (1988) |
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497 | (5) |
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Akashi's Basic Properties of Coincidence Degree |
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502 | (1) |
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Application to Multitivalued Boundary Value Problem for Elliptic Partial Differential Equation |
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503 | (4) |
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Applications of Equivalence Theorems with Single-Valued Mappings: An Approach to Non-Linear Elliptic Boundary Value Problems |
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507 | (18) |
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Tarafdar's Application to Elliptic Boundary Value Problems |
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521 | (4) |
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Further Results in Coincidence Degree Theory |
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525 | (3) |
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Tarafdar and Thompson's Theory of Bifurcation for the Solutions of Equations Involving Set-Valued Mapping |
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528 | (14) |
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Characteristic Value and Multiplicity |
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532 | (1) |
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Tarafdar and Thompson's Results on the Theory of Bifurcation |
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532 | (7) |
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Tarafdar and Thompson's Application on the Theory of Bifurcation |
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539 | (3) |
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Tarafdar and Thompson's Results on the Solvability of Non-Linear and Non-Compact Operator Equations |
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542 | (21) |
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Measure of Noncompactness and Set Contraction |
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542 | (4) |
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546 | (9) |
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Tarafdar and Thompson's (p, k)-Epi Mappings on the Whole Space |
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555 | (1) |
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Tarafdar and Thompson's Applications of (p, k)-Epi Mappings in Differential Equations |
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556 | (7) |
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Nonexpansive Types of Mappings and Fixed Point Theorems in Locally Convex Topological Vector Spaces |
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563 | (20) |
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Nonexpansive Types of Mappings in Locally Convex Topological Vector Spaces |
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563 | (8) |
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563 | (8) |
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Set-Valued Mappings of Nonexpansive Type |
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571 | (5) |
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Normal Structure and Fixed Point Theorems |
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572 | (3) |
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Another Definition of Nonexpansive Set-Valued Mapping and Corresponding Results on Fixed Point Theorems |
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575 | (1) |
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Fixed Point Theorems for Condensing Set-Valued Mappings on Locally Convex Topological Vector Spaces |
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576 | (7) |
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Measure of Precompactness and Non-Precompactness |
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577 | (1) |
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578 | (2) |
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580 | (3) |
| Bibliography |
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583 | (22) |
| Index |
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605 | |
