A fixed point theorem in Menger space through weak compatibility

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A fixed point theorem in Menger space through weak compatibility

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• Publié par: iwudawap
• Nombre de lectures: 67
• Langue: Français

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J. Math. Anal. Appl. 301 (2005) 439–448

www.elsevier.com/locate/jmaa

A fixed point theorem in Menger space through weak compatibility

a b,∗ Bijendra Singh , Shishir Jain

a S.S in Mathematics Vikram, University Ujjain (MP), India b Shri Vaishnav Institute of Technology and Science, Gram Baroli Post Alwasa, Indore (MP), India Received 10 May 2004

Submitted by William F. Ames

Abstract This paper contains a fixed point theorem for six self maps in Menger space. Our result generalizes and extends many known results in Menger spaces and metric spaces.
2004 Elsevier Inc. All rights reserved.

Keywords:Menger space;tnorm; Common fixed points; Compatible maps; Weakcompatible maps

1. Introduction

There have been a number of generalizations of metric space. One such generalization is Menger space initiated by Menger [6]. It is a probabilistic generalization in which we assign to any two pointsxandy, a distribution functionF x,y . Schweizer and Sklar [9] studied this concept and gave some fundamental results on this space. It is observed by many authors that contraction condition in metric space may be exactly translated into PMspace endowed with min norms. Sehgal and BharuchaReid [10] obtained a general ization of Banach Contraction Principle on a complete Menger space which is a milestone in developing fixedpoint theorems in Menger space.

* Corresponding author. Email address:[e-mail] (S. Jain).

0022247X/$ – see front matter
2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jmaa.2004.07.036