Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces

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Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces

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Author : Toka Diagana
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13

Almost Automorphic Type And Almost Periodic Type Functions In Abstract Spaces written by Toka Diagana and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.

This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.

Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations

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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-05-06

Almost Periodic And Almost Automorphic Solutions To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-06 with Mathematics categories.

This book discusses almost periodic and almost automorphic solutions to abstract integro-differential Volterra equations that are degenerate in time, and in particular equations whose solutions are governed by (degenerate) solution operator families with removable singularities at zero. It particularly covers abstract fractional equations and inclusions with multivalued linear operators as well as abstract fractional semilinear Cauchy problems.

Almost Periodic And Almost Automorphic Functions In Abstract Spaces

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Author : Gaston M. N'Guérékata
language : en
Publisher: Springer Nature
Release Date : 2021-05-28

Almost Periodic And Almost Automorphic Functions In Abstract Spaces written by Gaston M. N'Guérékata and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-28 with Mathematics categories.

This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and applications to evolution equations. Several generalizations have since been introduced in the literature, including the study of almost automorphic sequences, and the interplay between almost periodicity and almost automorphic has been exposed for the first time in light of operator theory, complex variable functions and harmonic analysis methods. As such, the time has come for a second edition to this work, which was one of the most cited books of the year 2001. This new edition clarifies and improves upon earlier materials, includes many relevant contributions and references in new and generalized concepts and methods, and answers the longtime open problem, "What is the number of almost automorphic functions that are not almost periodic in the sense of Bohr?" Open problems in non-locally convex valued almost periodic and almost automorphic functions are also indicated. As in the first edition, materials are presented in a simplified and rigorous way. Each chapter is concluded with bibliographical notes showing the original sources of the results and further reading.

Almost Periodicity And Almost Automorphy

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Author : Abdallah Afoukal
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03

Almost Periodicity And Almost Automorphy written by Abdallah Afoukal and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.

When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.

Almost Periodic Type Solutions

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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-03

Almost Periodic Type Solutions written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-03 with Mathematics categories.

Maybe for the first time in the existing literature, we investigate here the almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also investigate the generalized almost periodic type sequences and their applications in a rather detailed manner as well as many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions. We essenitally apply some results from the theory of C-regularized solution operator families to the abstract Volterra integro-differential-difference equations, contributing also to the theory of fractional calculus and fractional differential equations. The theory of abstract Volterra integro-differential equations and the theory of abstract Volterra difference equations are very attractive fields of research of many authors. The almost periodic features and the asymptotically almost periodic features of solutions to the abstract Volterra differential-difference equations in Banach spaces have been sought in many research articles published by now. The main aim of this monograph is to continue the work collected in my monographs published with W. de Gruyter recently by providing several new results about the existence and uniqueness of almost periodic type solutions to the abstract Volterra integro-differential-difference equations which could be solvable or unsolvable with respect to the highest derivative (order). We would like to particularly emphasize that this is probably the first research monograph devoted to the study of almost periodic type solutions to the abstract Volterra difference equations depending on several variables. We also consider here many new important spaces of (metrically) generalized almost periodic type spaces of sequences and functions, and their almost automorphic analogues. It is also worth noting that this is probably the first research monograph which concerns the generalized almost periodic type sequences and their applications in a rather detailed manner; for the first time in the existing literature, we also present here some applications of results from the theory of $C$-regularized solution operator families to the abstract Volterra difference equations. Fractional calculus and discrete fractional calculus are rapidly growing fields of theoretical and applied mathematics, which are incredibly important in modeling of various real phenomena appearing in different fields like aerodynamics, rheology, interval-valued systems, chaotic systems with short memory and image encryption and discrete-time recurrent neural networks. Many important research results regarding the abstract fractional differential equations and the abstract fractional difference equations in Banach spaces have recently been obtained by a great number of authors from the whole world. In this monograph, we also contribute to the theories of (discrete) fractional calculus, fractional differential-difference equations and multi-dimensional Laplace transform. Although the monograph is far from being complete, we have decided to quote almost eight hundred and fifty research articles which could be of some importance to the interested readers for further developments of the theory established here.

Metrical Almost Periodicity And Applications To Integro Differential Equations

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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-06-06

Metrical Almost Periodicity And Applications To Integro Differential Equations written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.

The theory of almost periodic functions is a very active field of research for scholars. This research monograph analyzes various classes of multi-dimensional metrically almost periodic type functions with values in complex Banach spaces. We provide many applications of our theoretical results to the abstract Volterra integro-differential inclusions in Banach spaces.

Selected Topics In Almost Periodicity

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Author : Marko Kostić
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22

Selected Topics In Almost Periodicity written by Marko Kostić and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.

Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.

Almost Automorphic And Almost Periodic Functions In Abstract Spaces

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Author : Gaston M. N'Guerekata
language : en
Publisher:
Release Date : 2014-01-15

Almost Automorphic And Almost Periodic Functions In Abstract Spaces written by Gaston M. N'Guerekata and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Almost Automorphic And Almost Periodic Functions In Abstract Spaces

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Author : Gaston M. N'Guérékata
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30

Almost Automorphic And Almost Periodic Functions In Abstract Spaces written by Gaston M. N'Guérékata and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Mathematics categories.

Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new results and applications. For the sake of clarity, and to spare the reader unnecessary technical hurdles, the concepts are studied using classical methods of functional analysis.

Advanced Functional Evolution Equations And Inclusions

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Author : Saïd Abbas
language : en
Publisher: Springer
Release Date : 2015-06-30

Advanced Functional Evolution Equations And Inclusions written by Saïd Abbas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-30 with Mathematics categories.

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.