Abstract
The aim of this paper is to prove some common fixed-point theorems for weakly compatible mappings in Menger spaces satisfying common property (E.A). Some examples are also given which demonstrate the validity of our results. As an application of our main result, we present a common fixed-point theorem for four finite families of self-mappings in Menger spaces. Our result is an improved probabilistic version of the result of Sedghi et al. [Gen. Math. 18:3-12, 2010]. MSC:54H25, 47H10, 54E70.
Highlights
In, Banach proved the principal contraction result [ ]
We prove some common fixed-point theorems for weakly compatible mappings in Menger space using the common property (E.A)
As an application of our main result, we extend the related results to four finite families of self-mappings in Menger spaces
Summary
In , Banach proved the principal contraction result [ ]. Jungck and Rhoades [ ] weakened the notion of compatibility by introducing the notion of weakly compatible mappings (extended by Singh and Jain [ ] to probabilistic metric space) and proved common fixed-point theorems without assuming continuity of the involved mappings in metric spaces. In , Aamri and Moutawakil [ ] introduced the notion of property (E.A) (extended by Kubiaczyk and Sharma [ ] to probabilistic metric space) for self-mappings which contained the class of noncompatible mappings due to Pant [ ]. Liu et al [ ] defined the notion of common property (E.A) (extended by Ali et al [ ] to probabilistic metric space) which contains the property (E.A) and proved several fixed-point theorems under hybrid contractive conditions. There has been continuous and intense research activity in fixed-point theory and there exists an extensive literature There has been continuous and intense research activity in fixed-point theory and there exists an extensive literature (e.g. [ – ] and the references therein)
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