Fixed Point Theory in Probabilistic Metric Spaces
Authors: Hadzic, O., Pap, Endre
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- About this book
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Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory.
Several themes run through this book. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces. Its recent development has had a strong influence upon the fixed point theory in probabilistic metric spaces.
In Chapter 1 some basic properties of t-norms are presented and several special classes of t-norms are investigated. Chapter 2 is an overview of some basic definitions and examples from the theory of probabilistic metric spaces. Chapters 3, 4, and 5 deal with some single-valued and multi-valued probabilistic versions of the Banach contraction principle. In Chapter 6, some basic results in locally convex topological vector spaces are used and applied to fixed point theory in vector spaces.
Audience: The book will be of value to graduate students, researchers, and applied mathematicians working in nonlinear analysis and probabilistic metric spaces.
- Table of contents (6 chapters)
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Triangular norms
Pages 1-46
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Probabilistic metric spaces
Pages 47-94
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Probabilistic B-contraction principles for single-valued mappings
Pages 95-153
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Probabilistic B-contraction principles for multi-valued mappings
Pages 155-184
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Hicks’ contraction principle
Pages 185-203
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Fixed Point Theory in Probabilistic Metric Spaces
- Authors
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- O. Hadzic
- Endre Pap
- Series Title
- Mathematics and Its Applications
- Series Volume
- 536
- Copyright
- 2001
- Publisher
- Springer Netherlands
- Copyright Holder
- Springer Science+Business Media Dordrecht
- eBook ISBN
- 978-94-017-1560-7
- DOI
- 10.1007/978-94-017-1560-7
- Hardcover ISBN
- 978-1-4020-0129-1
- Softcover ISBN
- 978-90-481-5875-1
- Edition Number
- 1
- Number of Pages
- IX, 273
- Topics
