• FIXED POINT THEOREM IN MENGER PROBABILISTIC METRIC SPACE

PIYUSH KUMAR TRIPATHI*

Abstract


The Banach fixed point theorem guarantees the existence of unique fixed point under a contraction mapping on a complete metric space. A similar theorem does not hold in a complete Menger Probabilistic metric space. The problem is that the triangular function in such spaces is not enough to guarantee that the sequence of iterates of a point under a certain map is Cauchy sequence. Two different approaches have been pursued. One is to identify those triangle functions which guarantee that the sequence of iterates is a Cauchy sequence. The other is to modify the original definition of contraction map. First this was done by Hicks. In this paper I prove some fixed point  in Menger space.

 


Full Text:

PDF


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
© 2010-2016 International Journal of Mathematical Archive (IJMA)
Copyright Agreement & Authorship Responsibility
Web Counter