Hemanta Kalita - Böcker

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 applicationPresents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applicationsHighlights fixed-point theory’s application to real-world problems and offers solutions to various complex challengesIntroduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integralDiscusses 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

The book focuses on the theory of fixed points, which is a foundation for many branches of pure and applied mathematics. Fixed point theorems have been studied in various function spaces. The book contains modern results on these theorems, investigated in generalized spaces such as S-metric spaces, convex metric spaces, and bipolar metric spaces, with applications in medical imaging. The nonlinear analysis presented in the book is valuable for modeling and solving real-world problems. It includes work on specific nonlinear operators and nonlinear fractional integral equations in Banach spaces. Relevant studies are also included on statistical convergence, inventory model modeling, computational techniques for Sentiment Analysis on Twitter Data, and Blood Management applications. The book is intended for young researchers interested in nonlinear analysis, fixed-point theory, and computational techniques.

This book contains proceedings of select chapters presented at the International Conference on Nonlinear Analysis & Computational Techniques (ICNACT-2024), held at VIT Bhopal University, Madhya Pradesh, India, from 8 to 10 August 2024. It discusses advances, emerging trends and theoretical developments in topics related to nonlinear analysis and computational techniques, including the introduction to new function spaces, such as a generalized Orlicz with Rao and Ren’s norm, the s-Young space and the controlled G-metric spaces. The book explains some relationships among different types of near linear spaces and introduces the strongly λ-summable functions.Nonlinear systems frequently require convergence and fixed point theorems. In this sense, the concept of q-lacunary almost statistical convergence is exposed. The book proposes a common coupled fixed point theorems, a few fixed point theorems for compatible mappings of type P and some applications on dynamic programming. In differential equations, some works extend Ostrowski-type inequalities; solution of the fractal nonlinear Klein–Gordon equation, study of a hybrid differential equation and the problem of exponential stability of the nonlinear Saint–Venant equation, finally provides a study of some properties for Cayley transform of operators. The book is useful to researchers in mathematics and applied sciences, engineers, graduate students, computational scientists, software developers and educators. They will benefit from this theory, which is essential for efficiently solving complex equations via the understanding, modeling and solving nonlinear problems and their theoretical and practical domains.

This book presents a systematic treatment of Henstock–Orlicz (or H-Orlicz) spaces with minimal assumptions on the Young function. H-Orlicz spaces contain non-absolute integrable functions called Henstock–Kurzweil integrable functions. Results from classical functional analysis are presented in detail, and new material is included on classical analysis. Extrapolation is used to prove, for example, the countable additivity of Henstock–Dunford integrable functions on H-Orlicz spaces are included. Relationships of modular convergence and norm convergence of H-Orlicz spaces are discussed. Finally, central geometrical results are provided for H-spaces, including uniformly convexity, reflexivity and the Radon–Nikodym property of the H–Orlicz spaces. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.