Fixed point theory in probabilistic metric spaces by Olga HadzМЊicМЃ

Cover of: Fixed point theory in probabilistic metric spaces | Olga HadzМЊicМЃ

Published by Kluwer Academic in Dordrecht, Boston .

Written in English

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Subjects:

  • Fixed point theory.,
  • Metric spaces.,
  • Probabilities.

Edition Notes

Includes bibliographical references (p. 245-267) and index.

Book details

Statementby Olga Hadžić and Endre Pap.
SeriesMathematics and its applications -- v. 536, Mathematics and its applications (Kluwer Academic Publishers) -- v. 536.
ContributionsPap, Endre.
Classifications
LC ClassificationsQA329.9 .H327 2001
The Physical Object
Paginationix, 273 p. ;
Number of Pages273
ID Numbers
Open LibraryOL21801288M
ISBN 101402001290
LC Control Number2001053848

Download Fixed point theory in probabilistic metric spaces

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 Cited by: The first is the theory of triangular norms (t-norms), which is Fixed point theory in probabilistic metric spaces book 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.

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. 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. A Menger probabilistic metric space (or random metric spaces) is a triple (X, F, T), where X is a nonempty set, T is a continuous t-norm, and F is a mapping from X × X into D + such that, if F x,y denotes the value of F at a point (x, y) ∈ X × X, the following conditions hold: for all x, y, z.

In this paper, we introduce a new concept of probabilistic metric space, which is a generalization of the Menger probabilistic metric space, and we investigate some topological properties of this space and related examples.

Also, we prove some fixed point theorems, which are the probabilistic versions of Banach’s contraction principle. Finally, we present an. The probabilistic version of the classical Banach Contraction Principle was proved in by Sehgal and Bharucha-Reid [V.M.

Sehgal, A.T. Bharucha-Reid, Fixed points of contraction mappings on PM spaces. Math. Syst. Theory 6, 97–]. Their fixed point theorem is further generalized by many authors. Abstract. Fixed point theory in probabilistic metric spaces book K.

Menger introduced the notion of a statistical metric space as a natural generalization of the notion of a metric space (M, d) in which the distance d(p, q) (p, q ∈ M) between p and q is replaced by a distribution function F p, q ∈ Δ +.F p,q (x) can be interpreted as the probability that the distance between p and q is less than by: 2.

This work is for giving the probabilistic aspect to the known b-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2), ), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.

In mathematical analysis. The Banach fixed-point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.

By contrast, the Brouwer fixed-point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point. The book will be useful to anyone who wishes to write a thesis on some aspect of fixed point theory in spaces .” (S.

Swaminathan, Mathematical Reviews, December, ) “This self-contained book provides the first systematic presentation of fixed point theory in G-metric spaces. Hicks TL () Fixed Point Theory in Probabilistic Metric Space ii.

Math Japonica, 44, [8] Menger K () Statistical Matrices, Proceedings of National Academy of Sciences of USA, 28, [9] Mihet D () Weak Hicks Contractions, Fixed Point Theory 6(1) [10].

The notion of E-space was introduced by Sherwood [16] in as a generalization of Menger space for random variables. For new results and applications of probabilistic analysis one can consult Constantin and Istrăţescu’s book [2]. New results in fixed point theory in probabilistic metric spaces can be find in [4] and in Hadzic’s book [3].

Fixed point theorems on soft metric spaces Article (PDF Available) in Journal of Fixed Point Theory and Applications 19(2) December with Reads How we measure 'reads'. 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.

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. The first is the theory of triangular norms (t-norms), which is closely related to fixed point theory in probabilistic metric spaces.

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are s: 1.

Mustafa, Z, Sims, B: Fixed point theorems for contractive mappings in complete G-metric spaces. Fixed Point Theory Appl.Article ID () Ciric, ´ L, Agarwal, RP, Samet, B: Mixed monotone generalized contractions in partially ordered probabilistic metric spaces.

Fixed Point Theory Appl.56 () 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. InBanach created a famous result called Banach contraction principle in the concept of the fixed point theory. Later, most of the authors intensively introduced many works regarding the fixed point theory in various of spaces.

The concept of a fuzzy metric space was introduced in different ways by some authors (see [2, 3]). A probabilistic metric space is a generalization of metric spaces where the distance has no longer values in non-negative real numbers, but in distribution functions. Let D+ be the set of all probability distribution functions F such that F(0) = 0 (F is a nondecreasing, left continuous mapping from into [0, 1] such that max(F) = 1).

The ordered pair (S,F) is said to be a probabilistic metric. On the other hand, an interesting class of problems in fixed point theory was addressed in recent times by use of gauge (control) functions.

There are several gauge (control) functions which have been used to extend Sehgal’s contraction in probabilistic metric spaces. Some examples of such applications are in [13–18]. In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space.

Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to.

Generalized contractions and fixed-point theorems. Publ Inst Math (Beograd) (NS) ; 12 (26)– Fan JX () On the generalizations of Ekeland’s variational principle and Caristi’s fixed point theorem.

In: The 6th National conference on the fixed point theory, variational inequalities and probabilistic metric spaces theory, Qingdao. some common fixed point theorems in metric spaces. InMihe [7] established a ţ fixed point theorem concerning probabilistic contractions satisfying an implicit relation.

The purpose of this paper is to prove a common fixed point theorem by combining the ideas of pointwise -weak commutativity and reciprocal continuity of mappings.

development of nonlinear analysis, the fixed point theory is one of the most important tool. InBackhtin introduced the concept of b-metric space. InCzerwik[5] extended the results of b-metric spaces. Using this idea many researcher presented generalization of the renowned banach fixed point theorem in the b-metric space.

Definition []: A set X is said to have a fixed point property(FPP) if each continuous mapping f: X —* X of this set into itself has a fixed point. In [], it is shown that fixed point property is a topological property. Historically the study of fixed point theory began in with a theorem given.

A COUNTEREXAMPLE TO \COMMON FIXED POINT THEOREM IN PROBABILISTIC QUASI-METRIC SPACE" DOREL MIHET» Abstract. We give a counterexample to the paper \Common flxed point theorem in probabilistic quasi-metric space" published in the flrst issue of this journal.

For details on the concepts used in the paper, the reader is referred to the book [1]. Metric Fixed Point Theory has proved a flourishing area of research for many mathematicians. This book aims to offer the mathematical community an accessible, self-contained account which can be used as an introduction to the subject and its development.

It will be understandable to a wide audience, including non-specialists, and provide a. This chapter discusses probabilistic metric spaces and some constructions methods of triangle functions.

One of the basic abstract tools in mathematics for solving nonlinear equations is the well-known classical Banach fixed point theorem. Recent Advances on Metric Fixed Point Theory This book consists of the Proceedings of the International Workshop on Metric Fixed Point Theory which was held at The University of Seville, September, For more information, please contact Professor T.

Dominguez Benavides via email at [email protected] Fixed point theory is a fascinating subject, with an enormous number of applications in various fields of mathematics.

Maybe due to this transversal character, I have always experienced some difficulties to find a book (unless expressly devoted to fixed points) treating the argument in a unitary fashion.

In most cases, I noticed. 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.

They established the existence and uniqueness of fixed points in a b-metric-like space as well as in a partially ordered b-metric-like space. In addition, as an application, they derived some new fixed point and coupled fixed point results in partial metric spaces, metric-like spaces, and b-metric spaces (see also [6–14]).

Chapter 6: Order-Theoretic Fixed Point Theory Fixed Point Theory / Completeness Conditions for Posets, Again / Iterative Fixed Point Theorems / Tarski's Fixed Point Theorems / Converse of the Knaster-Tarski Theorem / The Abian-Brown Fixed Point Theorem / Fixed Points of Order-Preserving Correspondences.

In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces.

The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results. A slight enlargement of the concept of 2‐metric space was given in [3], where B.

Dhage studied so called generalized metric spaces. In the present paper we have studied contraction conditions for mappings defined on a class of probabilistic metric space and fixed point theorems for such mappings. Continuous mappings in hyperconvex spaces Exercises 8 Metric Fixed Point Theory Contraction mappings Basic theorems for nonexpansive mappings A closer look at ßë Stability results in arbitrary spaces The Goebel-Karlovitz Lemma Orthogonal convexity Structure of the.

Fixed Point Theorems for Dissipative Mappings in Complete Probabilistic Metric Spaces. Mohamed A. Khamsi, Department of Mathematical Sciences, Vladik Ya. Kreinovich, Computer Science department, The University of Texas at El Paso. Abstract the physical notion of dissipative process gave rise to a mathematical notion of.

Sims B., Banach space geometry and the fixed point property(For a Post-Script version of this paper Click Here) Abstract: This is the text of four lectures given at the special international workshop on metric fixed point theory held at the University of Seville from September 25 -- 29, I would like to thank the University of Seville and the Workshop organizers for the .The answer is affirmative, and such spaces are called the D-symmetric quasi-metric.

These spaces are quite rich since they lie between the quasi-metric spaces and metric spaces, and they have proven to be very interesting topics for researchers who work in fixed point theory.

Dr. Andreea Fulga Prof. Erdal Karapinar Guest Editors.Home Browse by Title Periodicals Fuzzy Sets and Systems Vol.No. 1 Coincidence point theorems in probabilistic and fuzzy metric spaces article Coincidence point theorems in probabilistic and fuzzy metric spaces.

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