Published November 1, 2001
by Springer .
Written in English
|The Physical Object|
|Number of Pages||282|
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. 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. The book offers a detailed study of recent results in metric fixed point theory, presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations and covers basic definitions, mathematical preliminaries and proof of the main results. The first fixed point theorem in probabilistic metric spaces was proved by Sehgal and Barucha-Reid  for mappings f: S → S, where (S, F, T M) is a Menger space.
This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. An Introduction to Metric Spaces and Fixed Point Theory includes an extensive bibliography and an appendix which provides a complete summary of the concepts of set theory, including Zorn's Lemma, Tychonoff's Theorem, Zermelo's Theorem, and transfinite induction. These results are of interest in view of analogous results in metric spaces (see, for example  and ) and in view of recent activity in fixed point theory of probalistic metric spaces and. A comprehensive, basic level introduction to metric spaces and fixed point theory An Introduction to Metric Spaces and Fixed Point Theory presents a highly self-contained treatment of the subject that is accessible for students and researchers from diverse mathematical backgrounds, including those who may have had little training in mathematics beyond s: 2.
Schweizer and Sklar , developed the study of ﬁxed point theory in prob-abilistic metric spaces. In , Sehgal  initiated the study of contraction mapping theorem in probabilistic metric spaces. Several interesting and ele-gant result have been proved by various author in probabilistic metric spaces. In terms of content this text overlaps in places with three recent books on fixed point theory: Nonstandard Methods in Fixed Point Theory by A. Aksoy and M. A. Khamsi (Springer-Verlag, New York, Berlin, , pp.), Topics in Metric Fixed Point Theory . Probabilistic Metric Spaces by B. Schweizer, Probabilistic Metric Spaces Books available in PDF, EPUB, Mobi Format. Download Probabilistic Metric Spaces books, This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions. Presents up-to-date Banach space results. * Features an extensive bibliography for outside reading. * Provides detailed exercises that elucidate more introductory material.