Summability, Fixed Point Theory and Generalized Integrals with Applications

Hemanta Kalita, Mehmet Gurdal, Sanket Tikare, Talat Nazir

• Publisher: CRC Press
• Year: 2025
• eBook ISBN: 9781040352243
• Edition: 0
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics.

• Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application
• Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications
• Highlights fixed-point theory's application to real-world problems and offers solutions to various complex challenges
• Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral
• Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Contents
• Preface
• Editors
• Contributors
• Chapter 1 On Summability, Fixed Point Theory and Generalized Integrals
• Chapter 2 q− Bell Sequence Spaces and Associated Matrix Transformation
• Chapter 3 Almost Convergence via Bell Matrix
• Chapter 4 On Ideal Lacunary Statistical Convergence of Sequence in Gradual Normed Linear Spaces order α
• Chapter 5 On the Four-Dimensional Forward Difference Matrix
• Chapter 6 Absolute and Strong σ− Convergence defined by Modulus Function
• Chapter 7 Remarks on Ideal Variations of the Star-Hurewicz and Related Properties
• Chapter 8 Controlled v-Generalized Metric-type Space and Some Fixed Point Theorems with Application
• Chapter 9 Fixed Points of Graphic Contractions in b− Metric Spaces with a Directed Graph
• Chapter 10 Common Fixed Point Results via Simulation Functions and Solution of an Anti-Periodic Ordinary Differential Equation in Bipolar Metric Spaces
• Chapter 11 wt-Distance in Extended-Branciari b-Distance Metric Spaces and Application
• Chapter 12 Solution and Stability of New Type of Quadratic Multiplicative Functional Equation
• Chapter 13 Existence and Uniqueness of Solution of Nonlinear Fractional Dynamic Equation Involving Initial Condition on Time Scales
• Chapter 14 Remarks on Absolute and Non-absolute Integrability of Different Integrals for Multifunctions
• Chapter 15 Statistically Riemann Integrable Sequence of Functions on Time Scales
• Chapter 16 On McShane-type Integrals for Functions with Values in Topological Vector Spaces
• Chapter 17 On Existence and Uniqueness of Solutions of Volterra Integrals in Sense of McShane and Strong McShane
• Chapter 18 Weighted H-Orlicz Spaces and their Inclusion Properties
• Index