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Author: Józef Banaś
Publisher: Springer
ISBN: 8132218868
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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 Banaś
Publisher: Springer
ISBN: 8132218868
Category : Mathematics
Languages : en
Pages : 323
Get Book Here
Book Description
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
Publisher:
ISBN: 9788132218876
Category :
Languages : en
Pages : 328
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Book Description
Author: S. A. Mohiuddine
Publisher: CRC Press
ISBN: 1000610047
Category : Mathematics
Languages : en
Pages : 307
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Book Description
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
Publisher: CRC Press
ISBN: 1040013325
Category : Mathematics
Languages : en
Pages : 205
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Book Description
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
Publisher: Springer
ISBN: 9811037221
Category : Mathematics
Languages : en
Pages : 491
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Book Description
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: S. A. Mohiuddine
Publisher: Springer
ISBN: 9811330778
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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: S. A. Mohiuddine
Publisher: Springer Nature
ISBN: 9811961166
Category : Mathematics
Languages : en
Pages : 277
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Book Description
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: Saïd Abbas
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311055318X
Category : Mathematics
Languages : en
Pages : 359
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Book Description
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
Author: Oscar Castillo
Publisher: Springer Nature
ISBN: 9811981949
Category : Mathematics
Languages : en
Pages : 254
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Book Description
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: Said Abbas
Publisher: World Scientific
ISBN: 981126127X
Category : Mathematics
Languages : en
Pages : 326
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Book Description
This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.
