Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces

1. Front Matter

   Pages i-xiv

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2. Metric, Banach, and Hilbert Spaces

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   Pages 1-41

3. Linear Operators on Banach Spaces

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   Pages 43-77

4. Almost Periodic Functions

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   Pages 79-110

5. Almost Automorphic Functions

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   Pages 111-140

6. Pseudo-Almost Periodic Functions

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   Pages 141-166

7. Pseudo-Almost Automorphic Functions

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   Pages 167-188

8. Existence Results for Some Second-Order Differential Equations

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   Pages 189-207

9. Existence Results to Some Integrodifferential Equations

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   Pages 209-219

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

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    Pages 221-243

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

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    Pages 245-260

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

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    Pages 261-273

13. Stability Results for Some Higher-Order Difference Equations

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    Pages 275-288

14. Back Matter

    Pages 289-303

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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.

• Banach spaces
• Hilbert spaces
• abstract differential equations
• hypergroups
• metric spaces
• pseudo-periodic solutions
• ordinary differential equations
• partial differential equations

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)

• Department of Mathematics, Howard University, Washington, USA

  Toka Diagana

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