Fixed point theory in probabilistic metric spaces
著者
書誌事項
Fixed point theory in probabilistic metric spaces
（Mathematics and its applications, v. 536）
Kluwer Academic, c2010
- : pbk.
大学図書館所蔵 全1件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
Introduction. 1. Triangular norms. 2. Probabilistic metric spaces. 3. Probabilistic GBPIiGBP-contraction principles for single-valued mappings. 4. Probabilistic GBPIiGBP-contraction principles for multi-valued mappings. 5. Hicks' contraction principle. 6. Fixed point theorems in topological vector spaces and applications to random normed spaces. Bibliography. Index.
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