Topics in Fixed Point Theory

1. Front Matter

   Pages i-xi

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2. Introduction to Metric Fixed Point Theory

   • M. A. Khamsi

   Pages 1-32

3. Banach Contraction Principle and Its Generalizations

   • Abdul Latif

   Pages 33-64

4. Ekeland’s Variational Principle and Its Extensions with Applications

   • Qamrul Hasan Ansari

   Pages 65-100

5. Fixed Point Theory in Hyperconvex Metric Spaces

   • Rafael Espínola, Aurora Fernández-León

   Pages 101-158

6. An Introduction to Fixed Point Theory in Modular Function Spaces

   • W. M. Kozlowski

   Pages 159-222

7. Fixed Point Theory in Ordered Sets from the Metric Point of View

   • M. Z. Abu-Sbeih, M. A. Khamsi

   Pages 223-236

8. Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps

   • Hichem Ben-El-Mechaiekh

   Pages 237-272

9. Some Iterative Methods for Fixed Point Problems

   • Q. H. Ansari, D. R. Sahu

   Pages 273-300

10. Back Matter

    Pages 301-304

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The purpose of this contributed volume is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The book presents information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers. Key topics covered include Banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for set-valued maps, coincidence theorems, Lefschetz and Nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the Ekeland’s variational principle.

• Banach contraction theorem
• Ekeland variational principle
• Ky Fan and Kakutani theorems
• Lefschetz and Nielsen theories
• fixed point theory
• hyperconvex metric spaces
• iterative methods
• modular function spaces

From the book reviews:

“The book under review is the next presentation of main subjects in the theory. … The book has a good chance to be used as one more source of information for newcomers to the theory, students and researchers.” (K. Goebel, Mathematical Reviews, February, 2015)

• Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia

  Saleh Almezel

• Department of Mathematics, Aligarh Muslim University, Aligarh, India

  Qamrul Hasan Ansari

• Department of Mathematical Sciences, University of Texas at El Paso, El Paso, USA

  Mohamed Amine Khamsi

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