On Common Fixed Point For Compatible mappings in Menger Spaces

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Author(s) 
M. L. Joshi, Jay G. Mehta 

KEYWORDS 
Common fixed point, menger space, compatible maps, weakly compatible maps. 

ABSTRACT 
In this paper the concept of compatible map in menger space has been applied to prove common fixed point theorem. A fixed point theorem for self maps has been established using the concept of compatibility of pair of self maps.In 1942 Menger has introduced the theory of probabilistic metric spaces in which a distribution function was used instead of nonnegative real number as value of the metric. In 1966, Sehgal initiated the study of contraction mapping theorems in probabilistic metric spaces. Since then several generalizations of fixed point Sehgal and BharuchaReid, Sherwood, and Istratescu and Roventa have obtained several theorems in probabilistic metric space. The study of fixed point theorems in probabilistic metric spaces is useful in the study of existence of solutions of operator equations in probabilistic metric space and probabilistic functional analysis. In 2008, Altun and Turkoglu proved two common fixed point theorems on complete PMspace with an implicit relation. 

References 

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