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Multidimensional Integral Equations and Inequalities Edition. ed. [Kõva köide]

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Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

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From the reviews:

This book is concerned with integral equations and inequalities that involve functions of two or more independent variables. the book is self-contained and all results are presented in an easy-to-read way, it has been written for pure and applied professional mathematicians, engineers and physicists or the like. It certainly belongs on the bookshelf of specialists in analysis but the literature used is comprehensive, accurate and very up-to-date; many of the authors own works are cited, which shows his great expertise. (Nelson Jose Merentes, Mathematical Reviews, January, 2013)

Preface vii
Introduction 1(8)
1 Integral equations in two variables
9(50)
1.1 Introduction
9(1)
1.2 Basic integral inequalities
9(4)
1.3 Volterra-type integral equation
13(8)
1.4 Volterra-Fredholm-type integral equation
21(6)
1.5 Integrodifferential equations of hyperbolic-type
27(10)
1.6 Fredholm-type integrodifferential equation
37(9)
1.7 Miscellanea
46(11)
1.8 Notes
57(2)
2 Integral inequalities and equations in two and three variables
59(38)
2.1 Introduction
59(1)
2.2 Integral inequalities in two variables
59(6)
2.3 Integral inequalities in three variables
65(8)
2.4 Integral equation in two variables
73(5)
2.5 Integral equation in three variables
78(5)
2.6 Hyperbolic-type Fredholm integrodifferential equation
83(6)
2.7 Miscellanea
89(6)
2.8 Notes
95(2)
3 Mixed integral equations and inequalities
97(46)
3.1 Introduction
97(1)
3.2 Volterra-Fredholm-type integral inequalities I
97(11)
3.3 Volterra-Fredholm-type integral inequalities II
108(8)
3.4 Integral equation of Volterra-Fredholm-type
116(6)
3.5 Volterra-Fredholm-type integral equations
122(6)
3.6 General Volterra-Fredholm-type integral equations
128(7)
3.7 Miscellanea
135(6)
3.8 Notes
141(2)
4 Parabolic-type integrodifferential equations
143(48)
4.1 Introduction
143(1)
4.2 Basic integral inequalities
143(4)
4.3 Integrodifferential equation of Barbashin-type
147(8)
4.4 General integral equation of Barbashin-type
155(6)
4.5 Integrodifferential equation of the type arising in reactor dynamics
161(8)
4.6 Initial-boundary value problem for integrodifferential equations
169(10)
4.7 Miscellanea
179(10)
4.8 Notes
189(2)
5 Multivariable sum-difference inequalities and equations
191(46)
5.1 Introduction
191(1)
5.2 Sum-difference inequalities in two variables
191(7)
5.3 Sum-difference inequalities in three variables
198(6)
5.4 Multivariable sum-difference inequalities
204(7)
5.5 Sum-difference equations in two variables
211(11)
5.6 Volterra-Fredholm-type sum-difference equations
222(6)
5.7 Miscellanea
228(7)
5.8 Notes
235(2)
Bibliography 237(6)
Subject Index 243