Abstract
The aim of this paper is to generate two fixed point theorems in probabilistic 2-metric space by applying CLR’S-property and occasionally weakly compatible mappings (OWC), these two results generalize the theorem proved by V. K. Gupta, Arihant Jain and Rajesh Kumar. Further these results are justified with suitable examples.
Highlights
Menger [1] pioneered the statistical metric(SM) space theory
Further these results are justified with suitable examples
Altumn Turkoglu [4] proved some more results of SM-space by utilizing the implicit relation in multivalued mappings
Summary
Menger [1] pioneered the statistical metric(SM) space theory. One of the major achievements was the translation of probabilistic concepts into geometry. Sklar [2] introduced a new notion of a probabilistic-norm. This norm naturally generates topology, convergence ,continuity and completeness in SM-space. Mishra [3] used compatible mappings and generated some fixed points in Menger space. Xiaohong, Huacan He, and Yang Xu [5] employed the Schweizer-Sklar t-norm established fuzzy. Self-mappings; occasionally weakly compatible mappings; probabilistic 2-metric space; CLR’S-property. T. Bharucha-Reid [6] used classical Banach contraction to establish the first result of Menger space for coincidence points. Further some more results can be witnessed by using the concepts of sub sequentially continuous and semi compatible mappings in Menger space [10]
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