Bipan Hazarika - Böcker

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 spacesThe 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.

Advances in Mathematical Analysis and its Applications is designed as a reference text and explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. It discusses theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some topics are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more.Features:The book encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. It offers an understanding of research problems by presenting the necessary developments in reasonable detailsThe book also discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problemsContains applications on wavelets analysis and COVID-19 to show that mathematical analysis has interdisciplinary as well as real life applications.The book is aimed primarily at advanced undergraduates and postgraduate students studying mathematical analysis and mathematics in general. Researchers will also find this book useful.

This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc.• Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales• Connects several new areas of dynamic equations on time scales with applications in different fields• Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales• Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena• Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trendsThe text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics.

Non-Newtonian Sequence Spaces with Applications presents an alternative to the usual calculus based on multiplication instead of addition. This book is intended for graduate students and researchers with a special interest in non-Newtonian calculus, its applications, and related topics.Key features:Valuable material for postgraduate researchers studying non-Newtonian calculusSuitable as supplementary reading to a Computational Physics course

This book presents advanced research on quantum calculus, functional analysis, and their interdisciplinary applications. It focuses on solving complex challenges in areas such as quantum transport, carbon nanotubes, approximation theory, and renewable natural resources by providing cutting-edge developments in these specialised fields.

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. This book is meant for graduate students and researchers willing to expand their knowledge in these areas.

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. This book is meant for graduate students and researchers willing to expand their knowledge in these areas.

This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications.

This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications.

This book contains selected chapters on topology and dynamical systems and their interdisciplinary applications. Targeting researchers in interdisciplinary areas, the book covers contemporary interdisciplinary topics in topology and dynamical systems, such as closure functions, Partially Negative Dimensional Product (PNDP) manifolds, Khalimsky topological subspaces, neutrosophic topological space, ideal topological spaces, relator spaces, predator–prey symbiosis, cosmological models, and nanofluids.

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.

This book contains select chapters on topics related to nonlinear dynamics and functional analysis and their applications in quantum transport, carbon nanotubes, approximation theory, fixed point theory, quantum functional calculus, renewable natural resources, dynamic optimal control model and optimal control analysis. It focuses on bridging the gap between recent trends of interdisciplinary research in nonlinear dynamics and functional analysis. This book helps researchers, scientists and students in obtaining cutting-edge research in these areas and opens the pavement to apply nonlinear dynamics and functional analysis to solve interdisciplinary problems in several areas.

This comprehensive volume offers an in-depth exploration of advanced integration theories, extending beyond classical methods to unify and expand the field. Building on the foundational work of Jaroslav Kurzweil and Ralph Henstock, the book delves into the Henstock-Kurzweil and McShane gauge integrals, presenting a more intuitive and versatile alternative to the traditional Lebesgue integral. By bridging gaps in existing literature, the authors provide a rigorous treatment of integration on metric measure spaces, exploring critical concepts such as completeness, compactness, and Cousin's lemma.The book systematically introduces advanced topics, including the variational Henstock integral in locally convex spaces, the Riemann-Lebesgue integral for vector-valued functions, and generalizations of the Sugeno integral. Further chapters explore convergence in Banach spaces on time scales, set-valued integrals, and applications to harmonic analysis and partial differential equations, including solutions to the heat equation in distribution spaces.Notably, the text presents innovative approaches like the symmetric Laplace integral and the q-Homotopy Analysis Method for solving nonlinear integral equations, offering practical tools for modern analysis. Unified integral representations for generalized Mittag-Leffler functions further highlight the book's engagement with special functions.Ideal for researchers and advanced students in mathematical analysis, this book seamlessly integrates classical theories with modern advancements, offering both theoretical insights and practical applications across mathematics, physics, and engineering.

It also aims to pave the way for applying functional analysis and fixed-point theory to solve interdisciplinary problems in various domains, including but not limited to fractional calculus, integral equations, queuing theory, convex analysis, harmonic analysis and wavelet analysis.