<p>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.</p>

Almost Automorphic and Almost Periodic Functions in Abstract Spaces

Science & Math

N'Guérékata, Gaston M.

Mathematics

Springer

<p>Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]). New methods (method of invariant s- spaces, uniform spectrum), and new concepts (almost periodicity and almost automorphy in fuzzy settings) have been introduced in the literature. The range of applications include at present linear and nonlinear evolution equations, integro-differential and functional-differential equations, dynamical systems, etc...It has become imperative to take a bearing of the main steps of the the ory. That is the main purpose of this monograph. It is intended to inform the reader and pave the road to more research in the field. It is not a self contained book. In fact, [80] remains the basic reference and fimdamental source of information on these topics. Chapter 1 is an introductory one. However, it contains also some recent contributions to the theory of almost automorphic functions in abstract spaces. VIII Preface Chapter 2 is devoted to the existence of almost automorphic solutions to some Unear and nonUnear evolution equations. It con tains many new results. Chapter 3 introduces to almost periodicity in fuzzy settings with applications to differential equations in fuzzy settings. It is based on a work by B. Bede and S. G. Gal [40].</p>

Topics in Almost Automorphy

Reference

<p>This volume contains research and expository papers by African-American mathematicians on issues related to their involvement in the mathematical sciences. Little is known, taught, or written about African-American mathematicians. Information is lacking on their past and present contributions and on the qualitative and quantitative nature of their existence in and distribution throughout mathematics. This lack of information leads to a number of questions that have to date remained unanswered. This volume provides details and pointers to help answer some of these questions. </p>
<p>Features: </p>
<p>Research articles by distinguished African-American mathematicians. </p>
<p>Accomplishments of African-American researchers in the mathematical sciences. </p>
<p>Articles that explore issues important to the African-American community and to the mathematics community as a whole. </p>
<p>Inspiration for African-American students who wish to pursue advancement in the mathematical sciences.</p>

African Americans in Mathematics: Dimacs Workshop June 26-28, 1996 (DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE)

NSF Science and Technology Center in Discrete Mathematics and Theoretical Computer Science

Conference for African-American Researchers in the Mathematical Sciences (2nd : 1996 : Center for Discrete Mathematics and Theroretical Computer Science)

Amer Mathematical Society

Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists.

Topics in Fractional Differential Equations (Developments in Mathematics, Vol. 27) (Developments in Mathematics, 27)

Abbas, Saïd

Benchohra, Mouffak

<p>This is devoted to exploration of the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative.</p>

Topics in Fractional Differential Equations (Developments in Mathematics, 27)

<p>This book presents high-quality research from around the world on the theory and methods of linear or nonlinear evolution equations as well as their further applications. Equations dealing with the asymptotic behavior of solutions to evolution equations are included. The book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave Lagragian systems and integral equations.</p>

Leading-edge Research on Evolution Equations

Nova Science Pub Inc

This book is composed of lecture notes on courses to graduate students at various universities on the asymptotic behavior of differential equations. Anyone who has some acquaintance with differential equations in Banach spaces and Functional Analysis can read this book. It is primarily intended for graduate students and beginning researchers in the theory of evolution equations.

Lectures on the Asymptotic Behavior of Solutions of Differential Equations

Health, Fitness & Dieting

Van Minh, Nguyen

Yuan, Rong

Psychology & Counseling

<p><p>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 <i>Almost automorphic and almost periodic functions in abstract spaces</i> (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.&nbsp;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.</p> 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. <div><br /></div> <div>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. <div><br /></div> <div><br /> <br /></div> </div></p>

Almost Periodic and Almost Automorphic Functions in Abstract Spaces

See the best price to sell, buy, or rent books by N'Guérékata, Gaston M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by N'Guérékata, Gaston M.

See the best price to sell, buy, or rent books by N'Guérékata, Gaston M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Almost Automorphic and Almost Periodic Functions in Abstract Spaces

Topics in Almost Automorphy

African Americans in Mathematics: Dimacs Workshop June 26-28, 1996 (DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE)

Almost Automorphic and Almost Periodic Functions in Abstract Spaces

Topics in Almost Automorphy

Topics in Fractional Differential Equations (Developments in Mathematics, Vol. 27) (Developments in Mathematics, 27)

Topics in Fractional Differential Equations (Developments in Mathematics, 27)

Leading-edge Research on Evolution Equations

Lectures on the Asymptotic Behavior of Solutions of Differential Equations

Almost Periodic and Almost Automorphic Functions in Abstract Spaces