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E-grāmata: Sequence Space Theory with Applications

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  • Formāts: 306 pages
  • Izdošanas datums: 20-Jul-2022
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781000610086
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Sequence Space Theory with ApplicationsPalielināt
  • Formāts: 306 pages
  • Izdošanas datums: 20-Jul-2022
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781000610086
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"The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications"--

The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications.

Features

  • Discusses the Fibonacci and vector valued difference sequence spaces

  • Presents the solution of Volterra integral equation in Banach algebra

  • Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix

  • Presents the Tauberian theorems of double sequences

  • Discusses the paranormed Riesz difference sequence space of fractional order

    • Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces

    • The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.



    This book contains advance and modern techniques to define sequence spaces and obtain their applications.This book is aimed primarily at graduates and researchers studying sequence spaces. Students in mathematics and engineering would also find this book useful.

    Preface ix
    Editors xi
    Contributors xiii
    1 Hahn-Banach and Duality Type Theorems for Vector Lattice-Valued Operators and Applications to Subdifferential Calculus and Optimization
    		1(44)
    Antonio Boccuto
    1.1 Introduction
    		1(2)
    1.2 Basic Notions and Results
    		3(9)
    1.2.1 Relative interior points and convexity
    		3(1)
    1.2.2 Dual spaces of vector lattices and representation as spaces of continuous functions
    		4(3)
    1.2.3 The p-integral in vector lattice setting
    		7(2)
    1.2.4 A Chojnacki-type integral for vector lattice-valued functions
    		9(1)
    1.2.5 Basic assumptions and properties
    		9(3)
    1.3 The Main Results
    		12(23)
    1.4 Applications to Set Functions
    		35(10)
    Bibliography
    		38(7)
    2 Application of Measure of Noncompactness on Infinite System of Functional Integro-differential Equations with Integral Initial Conditions
    		45(18)
    Anupam Das
    2.1 Introduction
    		45(8)
    2.1.1 Preliminaries
    		46(1)
    2.1.2 Kuratowski measure of noncompactness
    		47(1)
    2.1.3 Axiomatic approach to the concept of a measure of noncompactness
    		47(1)
    2.1.4 Hausdorff measure of noncompactness
    		48(2)
    2.1.5 Condensing operators, compact operators and related results
    		50(3)
    2.2 Existence of Solution C(I, c0)
    		53(3)
    2.3 Existence of Solution C(I, 1)
    		56(3)
    2.4 Illustrative Example
    		59(2)
    2.5 Conclusion
    		61(2)
    Bibliography
    		61(2)
    3 α-Statistical Convergence of Interval Numbers of Order α
    		63(12)
    Ayhan Esi
    Ayten Esi
    3.1 Introduction
    		63(1)
    3.2 Main Results
    		64(11)
    Bibliography
    		72(3)
    4 Necessary and Sufficient Tauberian Conditions under which Convergence follows from (Ar,δ, p, q; 1, 1), (Ar,*, p, *; 1, 0) and (A*'δ, *, q; 0, 1) Summability Methods of Double Sequences
    		75(20)
    Qagla Kambak
    Ibrahim Canak
    4.1 Introduction
    		75(2)
    4.2 Auxiliary Results
    		77(2)
    4.3 Tauberian Theorems for the (Ar'δ, p, q; 1, 1) Summability Method
    		79(7)
    4.3.1 Proofs
    		82(4)
    4.4 Tauberian Theorems for the (Ar'*, p, *; 1, 0) Summability Method
    		86(6)
    4.4.1 Proofs
    		89(3)
    4.5 Tauberian Theorems for the (A*'δ, *, q; 0, 1) Summability Method
    		92(3)
    Bibliography
    		93(2)
    5 On New Sequence Spaces Related to Domain of the Jordan Totient Matrix
    		95(19)
    Emrah Evren Kara
    Necip Simsek
    Merve Ilkhan Kara
    5.1 Introduction and Background
    		95(4)
    5.2 The Domains of the Jordan Totient Matrix in the Spaces Co, c, ∞
    		99(2)
    5.3 The α-, β- and γ-Duals
    		101(3)
    5.4 Certain Matrix Transformations
    		104(10)
    Bibliography
    		111(3)
    6 A Study of Fibonacci Difference I-Convergent Sequence Spaces
    		114(25)
    Vakeel A. Khan
    Kamal M. A. S. Alshlool
    Sameera A. A. Abdullah
    6.1 Introduction and Preliminaries
    		114(7)
    6.1.1 Fibonacci sequence
    		115(6)
    6.2 Fibonacci Difference Sequence Spaces
    		121(8)
    6.3 Orlicz Fibonacci Difference Sequence Spaces
    		129(3)
    6.4 Paranormed Fibonacci Difference Sequence Spaces
    		132(7)
    Bibliography
    		135(4)
    7 Theory of Approximation for Operators in Intuitionistic Fuzzy Normed Linear Spaces
    		139(15)
    Nabanita Konwar
    Pradip Debnath
    7.1 Introduction
    		139(2)
    7.1.1 Background
    		140(1)
    7.1.2 Main goal
    		141(1)
    7.2 Basic Definitions
    		141(2)
    7.3 Definitions and Main Results
    		143(7)
    7.3.1 Essential definitions
    		143(1)
    7.3.2 Main results
    		144(1)
    7.3.3 Modified version of definitions of AP and BAP
    		145(1)
    7.3.4 Certain related results and examples
    		146(4)
    7.4 Conclusion
    		150(4)
    Bibliography
    		150(4)
    8 Solution of Volterra Integral Equations in Banach Algebras using Measure of Noncompactness
    		154(15)
    Hemant Kumar Nashine
    Anupam Das
    8.1 Introduction and Preliminaries
    		154(2)
    8.2 Fixed Point Results
    		156(6)
    8.3 Solvability of Volterra integral equation in Banach algebra
    		162(7)
    Bibliography
    		166(3)
    9 Solution of a pair of Nonlinear Matrix Equation using Fixed Point Theory
    		169(22)
    Hemant Kumar Nashine
    Sourav Shil
    9.1 Introduction and Preliminaries
    		169(1)
    9.2 Result 1
    		170(5)
    9.3 Result 2
    		175(4)
    9.3.1 Consequences
    		178(1)
    9.4 Application
    		179(3)
    9.5 Numerical Experiment
    		182(9)
    Bibliography
    		190(1)
    10 Sequence Spaces and Matrix Transformations
    		191(33)
    Ekrem Savas
    10.1 Introduction
    		191(2)
    10.2 On Strong σ-Convergence
    		193(5)
    10.3 σ-Regular Dual Summability Methods
    		198(4)
    10.3.1 Dual summability methods
    		199(1)
    10.3.2 σ-Regular summability methods
    		199(3)
    10.4 Some New Sequence Spaces
    		202(7)
    10.5 Some New Sequence Spaces Defined by Modulus
    		209(7)
    10.6 Matrix Transformations
    		216(8)
    Bibliography
    		220(4)
    11 Caratheodory Theory of Dynamic Equations on Time Scales
    		224(28)
    Sanket Tikare
    11.1 Introduction and Preliminaries
    		224(4)
    11.2 Caratheodory Solutions
    		228(8)
    11.3 Generalized Dynamic Equations
    		236(8)
    11.3.1 Henstock--Kurzweil Δ-integral
    		236(2)
    11.3.2 Existence and uniqueness of solutions
    		238(6)
    11.4 Dependency and Convergence of Solutions
    		244(8)
    Bibliography
    		250(2)
    12 Vector Valued Ideal Convergent Generalized Difference Sequence Spaces Associated with Multiplier Sequences
    		252(16)
    Binod Chandra Tripathy
    12.1 Introduction
    		252(1)
    12.2 Definitions and Preliminaries
    		253(3)
    12.2.1 Difference sequence spaces
    		254(1)
    12.2.2 Matrix transformation between sequence spaces
    		255(1)
    12.2.3 Vector valued sequence spaces
    		255(1)
    12.3 Ideal Convergence of Sequences
    		256(2)
    12.3.1 Statistically convergent sequence space
    		257(1)
    12.4 Sequence Spaces Associated with the Multiplier Sequences
    		258(2)
    12.4.1 Relation with real-life problems
    		259(1)
    12.4.2 Advantages
    		259(1)
    12.4.3 Vector valued generalized difference ideal convergent sequence spaces associated with the multiplier sequences
    		259(1)
    12.5 Main Results
    		260(3)
    12.6 Conclusion
    		263(5)
    Bibliography
    		264(4)
    13 Domain of Generalized Riesz Difference Operator of Fractional Order in Maddox's Space (p) and Certain Geometric Properties
    		268(21)
    Taj a Yaying
    Bipan Hazarika
    S. A. Mohiuddine
    13.1 Introduction
    		268(3)
    13.2 Paranormed Riesz Difference Sequence Space r*(p, ΔBq) of Fractional Order
    		271(4)
    13.3 The α-, β- and γ-Duals
    		275(3)
    13.4 Matrix Transformations
    		278(1)
    13.5 Certain Geometric Properties
    		279(10)
    Bibliography
    		283(6)
    Index 289
    S. A. Mohiuddine is a full professor of Mathematics at King Abdu- laziz University, Jeddah, Saudi Arabia. An active researcher, he has coau- thored three books, Convergence Methods for Double Sequences and Appli- cations (Springer, 2014), Advances in Summability and Approximation The- ory (Springer, 2018) and Soft Computing Techniques in Engineering, Health, Mathematical and Social Sciences (CRC Press, Taylor & Francis Group, 2021), and a number of chapters and has contributed over 140 research papers to var- ious leading journals. He is the referee of many scientific journals and member of the editorial board of various scientific journals, international scientific bod- ies and organizing committees. He has visited several international universities including Imperial College London, UK. He was a guest editor of a number of special issues for Abstract and Applied Analysis, Journal of Function Spaces and Scientific World Journal. His research interests are in the fields of sequence spaces, statistical convergence, matrix transformation, measures of noncom- pactness and approximation theory. His name was in the list of Worlds Top 2% Scientists (2020) prepared by Stanford University, California.

    Bipan Hazarika is presently a professor in the Department of Mathemat- ics at Gauhati University, Guwahati, India. He has worked at Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, India from 2005 to 2017. He was professor at Rajiv Gandhi University upto 10-08-2017. He received his Ph.D. degree from Gauhati University and his main research interests are in the field of sequences spaces, summability theory, applications of fixed point theory, fuzzy analysis and function spaces of non absolute integrable functions. He has published over 150 research papers in several international journals. He is an editorial board member of more than 5 international jour- nals and a regular reviewer of more than 50 different journals published from Springer, Elsevier, Taylor & Francis, Wiley, IOS Press, World Scientific, Amer- ican Mathematical Society, De Gruyter. He has published books on Differential Equations, Differential Calculus and Integral Calculus. He was the guest edi- tor of the special issue "Sequence spaces, Function spaces and Approximation Theory", in Journal of Function Spaces..
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