Abstract
Abstract In this paper, a new concept of the common property (E.A) for two hybrid pairs of mappings is introduced in Menger PM-spaces. Utilizing this concept, some common fixed point theorems, which shed some new light on the study of fixed point results for hybrid pairs in Menger PM-spaces, are obtained under strict contractive conditions. The corresponding results in metric spaces which generalize many known results are also obtained. Finally, an example is also given to exemplify our main results.
Highlights
The concept of a probabilistic metric space was initiated and studied by Menger which is a generalization of the metric space notion [, ]
Fixed point theory in a probabilistic metric space is an important branch of probabilistic analysis, which is closely related to the existence and uniqueness of solutions of differential equations and integral equations [, ]
The concept of compatible mappings in a Menger space was initiated by Mishra [ ], and since many fixed point results for compatible mappings and weakly compatible mappings have been studied [ – ]
Summary
The concept of a probabilistic metric space was initiated and studied by Menger which is a generalization of the metric space notion [ , ]. In , Aamri and Moutawakil defined a new property for a pair of mappings, i.e., the so-called property (E.A), which is a generalization of noncompatibility [ ] Using this property, some common fixed point theorems under strict contractive conditions in metric spaces have been given. Liu et al defined the concept of the common property (E.A) for single-valued as well as hybrid pairs of mappings in metric spaces and obtained many interesting results [ ]. Utilizing these concepts, many authors studied the existence of coincidence and fixed points in symmetric spaces [ – ].
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