Sequence Spaces And Measures Of Noncompactness With Applications To Differential And Integral Equations

Author : Józef Banaś,Mohammad Mursaleen
Publisher : Springer
Page : 315 pages
File Size : 49,7 Mb
Release : 2014-07-18
Category : Mathematics
ISBN : 9788132218869

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Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations by Józef Banaś,Mohammad Mursaleen Pdf

This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has many applications. The book discusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness; in particular, the Hausdorff measure of noncompactness has been applied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators. The book consists of eight self-contained chapters. Chapter 1 discusses the theory of FK spaces and Chapter 2 various duals of sequence spaces, which are used to characterize the matrix classes between these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties. The techniques associated with measures of noncompactness are applied to characterize the compact matrix operators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential and integral equations, which are obtained with the help of argumentations based on compactness conditions.

Author : Józef Bana,Mohammad Mursaleen
Publisher : Unknown
Page : 328 pages
File Size : 40,9 Mb
Release : 2014-08-31
Category : Electronic
ISBN : 8132218876

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Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations by Józef Bana,Mohammad Mursaleen Pdf

Author : S. A. Mohiuddine,Bipan Hazarika
Publisher : CRC Press
Page : 307 pages
File Size : 40,5 Mb
Release : 2022-07-20
Category : Mathematics
ISBN : 9781000610048

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Sequence Space Theory with Applications by S. A. Mohiuddine,Bipan Hazarika Pdf

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.

Author : S. A. Mohiuddine,M. Mursaleen,Dragan S. Djordjević
Publisher : CRC Press
Page : 222 pages
File Size : 48,7 Mb
Release : 2024-04-24
Category : Mathematics
ISBN : 9781040013366

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Measure of Noncompactness, Fixed Point Theorems, and Applications by S. A. Mohiuddine,M. Mursaleen,Dragan S. Djordjević Pdf

The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: • Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm • Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra • Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem • Discusses best proximity point results using measure of noncompactness and its applications • Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.

Author : Józef Banaś,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro
Publisher : Springer
Page : 487 pages
File Size : 50,7 Mb
Release : 2017-04-25
Category : Mathematics
ISBN : 9789811037221

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Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness by Józef Banaś,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro Pdf

This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.

Author : Bruno de Malafosse,Eberhard Malkowsky,Vladimir Rakočević
Publisher : Springer Nature
Page : 379 pages
File Size : 55,6 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : 9789811597428

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Operators Between Sequence Spaces and Applications by Bruno de Malafosse,Eberhard Malkowsky,Vladimir Rakočević Pdf

This book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and simplifications of complicated spaces involving these operators. In order to make it self-contained, comprehensive and of interest to a larger mathematical community, the authors have presented necessary concepts with results for advanced research topics. This book is intended for graduate and postgraduate students, teachers and researchers as a basis for further research, advanced lectures and seminars.

Author : Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal
Publisher : John Wiley & Sons
Page : 1050 pages
File Size : 53,5 Mb
Release : 2018-04-11
Category : Mathematics
ISBN : 9781119414339

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Mathematical Analysis and Applications by Michael Ruzhansky,Hemen Dutta,Ravi P. Agarwal Pdf

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Author : Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro
Publisher : Springer Nature
Page : 503 pages
File Size : 47,8 Mb
Release : 2021-06-05
Category : Mathematics
ISBN : 9789813366473

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Advances in Metric Fixed Point Theory and Applications by Yeol Je Cho,Mohamed Jleli,Mohammad Mursaleen,Bessem Samet,Calogero Vetro Pdf

This book collects papers on major topics in fixed point theory and its applications. Each chapter is accompanied by basic notions, mathematical preliminaries and proofs of the main results. The book discusses common fixed point theory, convergence theorems, split variational inclusion problems and fixed point problems for asymptotically nonexpansive semigroups; fixed point property and almost fixed point property in digital spaces, nonexpansive semigroups over CAT(κ) spaces, measures of noncompactness, integral equations, the study of fixed points that are zeros of a given function, best proximity point theory, monotone mappings in modular function spaces, fuzzy contractive mappings, ordered hyperbolic metric spaces, generalized contractions in b-metric spaces, multi-tupled fixed points, functional equations in dynamic programming and Picard operators. This book addresses the mathematical community working with methods and tools of nonlinear analysis. It also serves as a reference, source for examples and new approaches associated with fixed point theory and its applications for a wide audience including graduate students and researchers.

Author : S. A. Mohiuddine,Tuncer Acar
Publisher : Springer
Page : 241 pages
File Size : 49,7 Mb
Release : 2018-12-30
Category : Mathematics
ISBN : 9789811330773

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Advances in Summability and Approximation Theory by S. A. Mohiuddine,Tuncer Acar Pdf

This book discusses the Tauberian conditions under which convergence follows from statistical summability, various linear positive operators, Urysohn-type nonlinear Bernstein operators and also presents the use of Banach sequence spaces in the theory of infinite systems of differential equations. It also includes the generalization of linear positive operators in post-quantum calculus, which is one of the currently active areas of research in approximation theory. Presenting original papers by internationally recognized authors, the book is of interest to a wide range of mathematicians whose research areas include summability and approximation theory. One of the most active areas of research in summability theory is the concept of statistical convergence, which is a generalization of the familiar and widely investigated concept of convergence of real and complex sequences, and it has been used in Fourier analysis, probability theory, approximation theory and in other branches of mathematics. The theory of approximation deals with how functions can best be approximated with simpler functions. In the study of approximation of functions by linear positive operators, Bernstein polynomials play a highly significant role due to their simple and useful structure. And, during the last few decades, different types of research have been dedicated to improving the rate of convergence and decreasing the error of approximation.

Author : Pradip Debnath,H. M. Srivastava,Poom Kumam,Bipan Hazarika
Publisher : Springer Nature
Page : 358 pages
File Size : 41,6 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 9789811906688

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Fixed Point Theory and Fractional Calculus by Pradip Debnath,H. M. Srivastava,Poom Kumam,Bipan Hazarika Pdf

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

Author : S. A. Mohiuddine,M. Mursaleen,Dragan S. Djordjević
Publisher : CRC Press
Page : 205 pages
File Size : 47,8 Mb
Release : 2024-04-24
Category : Mathematics
ISBN : 9781040013328

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Measure of Noncompactness, Fixed Point Theorems, and Applications by S. A. Mohiuddine,M. Mursaleen,Dragan S. Djordjević Pdf

The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem Discusses best proximity point results using measure of noncompactness and its applications Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.

Author : S. A. Mohiuddine,Bipan Hazarika,Hemant Kumar Nashine
Publisher : Springer Nature
Page : 277 pages
File Size : 42,8 Mb
Release : 2022-12-07
Category : Mathematics
ISBN : 9789811961168

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Approximation Theory, Sequence Spaces and Applications by S. A. Mohiuddine,Bipan Hazarika,Hemant Kumar Nashine Pdf

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. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.

Author : Santo Banerjee,Asit Saha
Publisher : Springer Nature
Page : 1433 pages
File Size : 47,7 Mb
Release : 2022-10-06
Category : Science
ISBN : 9783030997922

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Nonlinear Dynamics and Applications by Santo Banerjee,Asit Saha Pdf

This book covers recent trends and applications of nonlinear dynamics in various branches of society, science, and engineering. The selected peer-reviewed contributions were presented at the International Conference on Nonlinear Dynamics and Applications (ICNDA 2022) at Sikkim Manipal Institute of Technology (SMIT) and cover a broad swath of topics ranging from chaos theory and fractals to quantum systems and the dynamics of the COVID-19 pandemic. Organized by the SMIT Department of Mathematics, this international conference offers an interdisciplinary stage for scientists, researchers, and inventors to present and discuss the latest innovations and trends in all possible areas of nonlinear dynamics.

Author : Oscar Castillo,Uttam Kumar Bera,Dipak Kumar Jana
Publisher : Springer Nature
Page : 254 pages
File Size : 47,6 Mb
Release : 2023-05-23
Category : Mathematics
ISBN : 9789811981944

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Applied Mathematics and Computational Intelligence by Oscar Castillo,Uttam Kumar Bera,Dipak Kumar Jana Pdf

This book contains select papers presented at the International Conference on Applied Mathematics and Computational Intelligence (ICAMCI-2020), held at the National Institute of Technology Agartala, Tripura, India, from 19–20 March 2020. It discusses the most recent breakthroughs in intelligent techniques such as fuzzy logic, neural networks, optimization algorithms, and their application in the development of intelligent information systems by using applied mathematics. The book also explains how these systems will be used in domains such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and complicated problems in optimization. The book publishes new developments and advances in various areas of type-3 fuzzy, intuitionistic fuzzy, computational mathematics, block chain, creak analysis, supply chain, soft computing, fuzzy systems, hybrid intelligent systems, thermos-elasticity, etc. The book is targeted to researchers, scientists, professors, and students of mathematics, computer science, applied science and engineering, interested in the theory and applications of intelligent systems in real-world applications. It provides young researchers and students with new directions for their future study by exchanging fresh thoughts and finding new problems.

Author : Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 359 pages
File Size : 40,5 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110553185

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Implicit Fractional Differential and Integral Equations by Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson Pdf

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations