Sequence Space Theory with Applications

✍ Scribed by S. A. Mohiuddine, Bipan Hazarika

• Publisher: CRC Press/Chapman & Hall
• Year: 2022
• Tongue: English
• Leaves: 307
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Editors
Contributors
1. Hahn-Banach and Duality Type Theorems for Vector Lattice-Valued Operators and Applications to Subdifferential Calculus and Optimization
1.1. Introduction
1.2. Basic Notions and Results
1.2.1. Relative interior points and convexity
1.2.2. Dual spaces of vector lattices and representation as spaces of continuous functions
1.2.3. The p-integral in vector lattice setting
1.2.4. A Chojnacki-type integral for vector lattice-valued functions
1.2.5. Basic assumptions and properties
1.3. The Main Results
1.4. Applications to Set Functions
Bibliography
2. Application of Measure of Noncompactness on Infinite System of Functional Integro-differential Equations with Integral Initial Conditions
2.1. Introduction
2.1.1. Preliminaries
2.1.2. Kuratowski measure of noncompactness
2.1.3. Axiomatic approach to the concept of a measure of noncompactness
2.1.4. Hausdor measure of noncompactness
2.1.5. Condensing operators, compact operators and related results
2.2. Existence of Solution C(I, c0)
2.3. Existence of Solution C(I, l1)
2.4. Illustrative Example
2.5. Conclusion
Bibliography
3. -Statistical Convergence of Interval Numbers of Order a
3.1. Introduction
3.2. Main Results
Bibliography
4. Necessary and Sufficient Tauberian Conditions under which Convergence follows from (Ar,s,p,q; 1,1), (Ar,,p,; 1,0) and (A,s,,q; 0,1) Summability Methods of Double Sequences
4.1. Introduction
4.2. Auxiliary Results
4.3. Tauberian Theorems for the (Ar,s,p,q; 1,1) Summability Method
4.3.1. Proofs
4.4. Tauberian Theorems for the (Ar,,p,; 1,0) Summability Method
4.4.1. Proofs
4.5. Tauberian Theorems for the (A,s,,q; 0,1) Summability Method
Bibliography
5. On New Sequence Spaces Related to Domain of the Jordan Totient Matrix
5.1. Introduction and Background
5.2. The Domains of the Jordan Totient Matrix in the Spaces c0, c,l
5.3. The a-, b- and y-Duals
5.4. Certain Matrix Transformations
Bibliography
6. A Study of Fibonacci Difference I-Convergent Sequence Spaces
6.1. Introduction and Preliminaries
6.1.1. Fibonacci sequence
6.2. Fibonacci Difference Sequence Spaces
6.3. Orlicz Fibonacci Difference Sequence Spaces
6.4. Paranormed Fibonacci Difference Sequence Spaces
Bibliography
7. Theory of Approximation for Operators in Intuitionistic Fuzzy Normed Linear Spaces
7.1. Introduction
7.1.1. Background
7.1.2. Main goal
7.2. Basic Definitions
7.3. Definitions and Main Results
7.3.1. Essential definitions
7.3.2. Main results
7.3.3. Modified version of de nitions of AP and BAP
7.3.4. Certain related results and examples
7.4. Conclusion
Bibliography
8. Solution of Volterra Integral Equations in Banach Algebras using Measure of Noncompactness
8.1. Introduction and Preliminaries
8.2. Fixed Point Results
8.3. Solvability of Volterra integral equation in Banach algebra
Bibliography
9. Solution of a pair of Nonlinear Matrix Equation using Fixed Point Theory
9.1. Introduction and Preliminaries
9.2. Result 1
9.3. Result 2
9.3.1. Consequences
9.4. Application
9.5. Numerical Experiment
Bibliography
10. Sequence Spaces and Matrix Transformations
10.1. Introduction
10.2. On Strong o-Convergence
10.3. o-Regular Dual Summability Methods
10.3.1. Dual summability methods
10.3.2. o-Regular summability methods
10.4. Some New Sequence Spaces
10.5. Some New Sequence Spaces Defined by Modulus
10.6. Matrix Transformations
Bibliography
11. Caratheodory Theory of Dynamic Equations on Time Scales
11.1. Introduction and Preliminaries
11.2. Caratheodory Solutions
11.3. Generalized Dynamic Equations
11.3.1. Henstock-Kurzweil
-integral
11.3.2. Existence and uniqueness of solutions
11.4. Dependency and Convergence of Solutions
Bibliography
12. Vector Valued Ideal Convergent Generalized Difference Sequence Spaces Associated with Multiplier Sequences
12.1. Introduction
12.2. Definitions and Preliminaries
12.2.1. Difference sequence spaces
12.2.2. Matrix transformation between sequence spaces
12.2.3. Vector valued sequence spaces
12.3. Ideal Convergence of Sequences
12.3.1. Statistically convergent sequence space
12.4. Sequence Spaces Associated with the Multiplier Sequences
12.4.1. Relation with real-life problems
12.4.2. Advantages
12.4.3. Vector valued generalized difference ideal convergent sequence spaces associated with the multiplier sequences
12.5. Main Results
12.6. Conclusion
Bibliography
13. Domain of Generalized Riesz Difference Operator of Fractional Order in Maddox's Space l(p) and Certain Geometric Properties
13.1. Introduction
13.2. Paranormed Riesz Di erence Sequence Space rt(p,
Bq) of Fractional Order
13.3. The a-, b- and y-Duals
13.4. Matrix Transformations
13.5. Certain Geometric Properties
Bibliography
Index