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Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces

  • Book
  • © 2013

Overview

Authors:
  1. Toka Diagana

    1. Department of Mathematics, Howard University, Washington, USA

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  • Introduces several new classes of functions as well as their applications to first, second, third, and higher-order differential equations

  • Contains material which has never before been presented in a book format

  • Can be used for beginning graduate and advanced undergraduate courses

  • Includes supplementary material: sn.pub/extras

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Metric, Banach, and Hilbert Spaces

    • Toka Diagana
    Pages 1-41

  3. Linear Operators on Banach Spaces

    • Toka Diagana
    Pages 43-77

  4. Almost Periodic Functions

    • Toka Diagana
    Pages 79-110

  5. Almost Automorphic Functions

    • Toka Diagana
    Pages 111-140

  6. Pseudo-Almost Periodic Functions

    • Toka Diagana
    Pages 141-166

  7. Pseudo-Almost Automorphic Functions

    • Toka Diagana
    Pages 167-188

  8. Existence Results for Some Second-Order Differential Equations

    • Toka Diagana
    Pages 189-207

  9. Existence Results to Some Integrodifferential Equations

    • Toka Diagana
    Pages 209-219

  10. Existence of C (m)-Pseudo-Almost Automorphic Solutions

    • Toka Diagana
    Pages 221-243

  11. Pseudo-Almost Periodic Solutions to Some Third-Order Differential Equations

    • Toka Diagana
    Pages 245-260

  12. Pseudo-Almost Automorphic Solutions to Some Sobolev-Type Equations

    • Toka Diagana
    Pages 261-273

  13. Stability Results for Some Higher-Order Difference Equations

    • Toka Diagana
    Pages 275-288

  14. Back Matter

    Pages 289-303
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Keywords

About this book

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.

Reviews

From the book reviews:

“This book is a nice text for those interested in the topics of almost automorphy and almost periodicity in abstract spaces. … It is worth mentioning that some results are new or not easily accessible in the mathematical literature, which makes the book even more interesting. In greater detail, the book is structured in twelve chapters and an appendix.” (Tomás Caraballo, Mathematical Reviews, June, 2014)

Authors and Affiliations

  • Department of Mathematics, Howard University, Washington, USA

    Toka Diagana

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