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E-raamat: Double Sequence Spaces and Four-Dimensional Matrices [Taylor & Francis e-raamat]

, (Professor, Inonu University, Turkey)
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Double Sequence Spaces and Four-Dimensional MatricesSuurem pilt
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Double Sequence Spaces and Four-Dimensional Matrices provides readers with a clear introduction to the spaces of double sequences and series, as well as their properties. The book then goes beyond this to investigate paranormed double sequence spaces and their algebraic and topological properties, triangle matrices and their domains in certain spaces of double sequences, dual spaces of double sequence spaces, and matrix transformations between double sequence spaces and related topics.

Each chapter contains a conclusion section highlighting the importance of results and pointing out possible new ideas that can be studied further.

Features











Suitable for students at graduate or post-graduate level and researchers





Investigates different types of summable spaces and computes their duals





Characterizes several four-dimensional matrix classes transforming one summable space into other





Discusses several algebraic and topological properties of new sequence spaces generated by the domain of triangles.
Foreword ix
Preface xi
Authors xiii
List of Abbreviations and Symbols
xv
1 Spaces of Double Sequences and Series
1(36)
1.1 Double Sequence Spaces
1(8)
1.2 Double Series Spaces
9(5)
1.3 Four-Dimensional Infinite Matrices
14(4)
1.4 Some Topological Properties of the Spaces Almost Null and Almost Convergent Double Sequences
18(4)
1.5 Puesz Summability of Double Series
22(5)
1.6 Abel Summability of Double Series
27(5)
1.7 Conclusion
32(3)
1.8 Exercises
35(2)
2 Some Paranormed Double Sequence Spaces
37(22)
2.1 Preliminaries, Background and Notations
37(1)
2.2 The Double Sequence Spaces Cp(t) and Cbp(t)
38(8)
2.3 Paranormed Space Mu(t) of Double Sequences
46(2)
2.4 Double Sequence Spaces Cp0(t), Cbp0(t) and Lu(t)
48(4)
2.5 Paranormed Spaces Cr(t), Cr0(t), Ctr(t) and Ctr0(t)
52(3)
2.6 Conclusion
55(1)
2.7 Exercises
56(3)
3 Matrix Domain in Double Sequence Spaces
59(42)
3.1 Preliminaries, Background and Notations
59(1)
3.2 Certain Paranormed Difference Spaces of Double Sequences
59(6)
3.3 Double Sequence Spaces BS, BS(t), CS and BV
65(10)
3.4 Difference Spaces of Almost Convergent and Strongly Almost Convergent Double Sequences
75(5)
3.5 Absolutely s-Summable Double Sequences
80(4)
3.6 Riesz Domains in Some Double Sequence Spaces
84(9)
3.7 Domain of Euler Mean in the Space of Absolutely s-summable Double Sequences With 0 >'s > 1
93(3)
3.8 Conclusion
96(3)
3.9 Exercises
99(2)
4 Dual Spaces of Double Sequence Spaces
101(40)
4.1 Preliminaries, Background and Notations
101(1)
4.2 Dual Spaces of Double Series
102(3)
4.3 Dual Spaces of Mu(t)
105(5)
4.4 Dual Spaces of Cp0(t), Cbp(t) and Cbp0(t)
110(2)
4.5 Dual Spaces of the Space u(t)
112(8)
4.6 The Alpha-dual of the Space Mu(t)
120(3)
4.7 Dual Spaces of the Spaces Cf(Δ), Cf0(Δ) and
123(2)
4.8 Dual Spaces of the Spaces CT(t), Cr0(t), Ctr(t) and Ctro(t)
125(5)
4.9 Dual Spaces of the Spaces BVa and SS
130(3)
4.10 Dual Spaces of Riesz Spaces Rqt(Mu), Rqt(Cs) and Rqt(Ca)
133(3)
4.11 Dual Spaces of Εp,r Spaces
136(2)
4.12 Conclusion
138(1)
4.13 Exercises
139(2)
5 Matrix Transformations Between Double Sequence Spaces
141(77)
5.1 Preliminaries, Background and Notations
141(5)
5.2 Characterizations of Some Matrix Classes
146(34)
5.3 Mercerian and Steinhaus Type Theorems for Four-Dimensional Matrices
180(5)
5.4 Comparison of Four-Dimensional Summability Methods
185(5)
5.5 Four-Dimensional Usual Dual Summability Methods
190(2)
5.6 Four-Dimensional Dual Summability Methods of the New Sort
192(9)
5.7 Summability of Unbounded Double Sequences
201(7)
5.8 Some Tauberian Theorems for Four-Dimensional Euler and Borel Summabilities
208(6)
5.9 Conclusion
214(2)
5.10 Exercises
216(2)
Bibliography 218(13)
Index 231
Dr. Feyzi Baar is a Professor Emeritus since July 2016 at nönü University, Turkey. He has published three books for graduate students and researchers and more than 160 scientific papers in the field of summability theory, sequence spaces, FK-spaces, Schauder bases, dual spaces, matrix transformations, spectrum of certain linear operators represented by a triangle matrix over some sequence spaces, the alpha-, beta- and gamma-duals and some topological properties of the domains of some double and four-dimensional triangles in certain spaces of single and double sequences and sets of the sequences of fuzzy numbers. Nowadays, Professor Baar works on the development of sequences and series, and the basic concepts of summability in non-newtonian calculus. He has guided 17 MA and 10 Ph.D. students and served as a referee for 141 international scientific journals. He is reviewer Mathematical Reviews since 2007 and Zentralblatt MATH, and the member of editorial boards of 21 scientific journals. He is also a member of scientific committees of 17 mathematics conferences, delivered talks at 14 different universities as an invited speaker, and worked on 10 scientific project, and participated in more than 70 mathematics symposiums with papers.

Dr. Medine Yeilkayagil Savac is an Associated Professor at Uak University. She has published more than 25 scientific papers in the field of summability theory, sequence spaces, FK-spaces, Schauder bases, dual spaces, matrix transformations, spectrum of certain linear operators represented by a triangle matrix over some sequence spaces, the alpha-, beta- and gamma-duals and some topological properties of the domains of some double and four-dimensional triangles in certain spaces of single and double sequences. She is reviewer Mathematical Reviews since 2017 and reviews in 11 international
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