Common Fixed Point for Two Pairs of Mappings Satisfying (E.A) Property in Generalized Metric Spaces

Abstract

Recently, Abbas et al. (2012) obtained some unique common fixed-point results for a pair of mappings satisfying (E.A) property under certain generalized strict contractive conditions in the framework of a generalized metric space. In this paper, we present common coincidence and common fixed points of two pairs of mappings when only one pair satisfies (E.A) property in the setup of generalized metric spaces. We present some examples to support our results. We also study well-posedness of common fixed-point problem.

Common coupled fixed point theorems for hybrid pair of mappings satisfying an implicit relation with application

“…, (23) and other conditions of Corollary 8 improve and generalize the results of Kaneko [18] and Kaneko and Sessa [19]. Now we give an example to illustrate our main theorems.…”

“…Then F and g have a common coupled fixed point. Remark 2 Conditions (22), (23) and other conditions of Corollary 6 improve and generalize the results of Kamran [17].…”

Fixed Point Theory in Metric Type Spaces

“…In [129], Long, Abbas, Nazir and Radenović proved the following result, where they used the notion of weak compatibility introduced in Definition 6.4.1 and the concept of the point of coincidence given in Definition 6.4.2. hold for all x; y 2 X, where 2 F alt and 2 F 0 alt . Suppose that one of the pairs .f ; S/ and .g; T/ satisfies the (E.A) property and one of the subspace f .X/, g .X/, S .X/, T .X/ is closed in X.…”

C-class functions and remarks on fixed points of weakly compatible mappings in G-metric spaces satisfying common limit range property

“…Many mathematicians studied extensively various results on G-metric spaces by using the concept of weak commutativity, compatibility, non-compatibility and weak compatibility for single valued mappings satisfying different contractive conditions (cf. [2]- [8], [10]- [12], [15], [17]- [29]). Branciari [9] obtained a fixed point result for a single mapping satisfying an analogue of Banach's contraction principle for an integral type inequality.…”