Abstract
Objective/Aim: To generate a fixed point theorem in probabilistic 2-metric space. Method: By employing strong semi compatible mappings and sub sequentially continuous mappings. Findings: Generated unique common fixed point theorem and substantiated with appropriate example. Novelty/ Improvement: The concepts of strong semi compatible mappings and sub sequentially continuous mappings are weaker than existing conditions like weakly compatible mappings which generalizes the theorem of V. K. Gupta, Arihant Jain and Rajesh kumar. Keywords: Strong semi compatible; sub sequentially continuous; Probabilistic 2metric space; conditional semi compatible; conditional compatible
Highlights
The analysis is main branch of mathematics, one of its main ingredient is to give the solution of problems in all fields which is based on fixed points theory
This turned way to extraction of fixed point theorems with minimal effort
The major achievement was the introduction of compatibility concept in Menger space by Mishra (3), resulting the flood of many fixed point theorems established
Summary
The analysis is main branch of mathematics, one of its main ingredient is to give the solution of problems in all fields which is based on fixed points theory. Some more results were obtained on this area by Martinez et al (4) In this connection searching of fixed points theorems led to the arrival of the concepts of continuity, reciprocal continuity, sub sequential continuity, semi compatibility, conditional semi compatibility and strong semi compatibility in Menger space like in (5). These concepts have been extended to generate some more results like in (6). Chauhan (7) introduced the notion of occasionally weakly compatible maps in megner space In this context many researchers are focusing on the existence of fixed point theorems and their applications in different ways(8).
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