Common Fixed Point for Three Pairs of Self-Maps Satisfying Common (E.A) Property in Generalized Metric Spaces

Abstract

Using the concept of common (E.A) property, we prove a common fixed point theorem for three pairs of weakly compatible self-maps satisfying a new contractive condition in the framework of a generalized metric space. Our results do not rely on any commuting or continuity condition of mappings. An example is provided to support our result. The results obtained in this paper differ from the recent relative results in the literature.

Common fixed point theorems for a class of maps of Φ -contraction in generalized metric spaces

“…Remark 2.3. Theorem 2.1 improves and extends the corresponding results of [7] and [10] in three aspects:…”

Common Fixed Point Theorem for Pair of Mappings Satisfying Common (E.A)-PROPERTY in Complete Metric Spaces With Application Rakesh Tiwari and Shashi Thakur

“…Many authors established fixed points results for different classes of mappings on metric spaces. ( [6], [12], [15])…”

“…In 2005, Liu et al [11] defined the notion of common (E.A) property. Many authors established common fixed point theorems by using common (E.A) property in the setup of metric spaces and variants of metric spaces [3,5,6,13]. Recently, R. Tiwari and S. Gupta [19] proved some new common fixed point theorems in metric spaces for weakly compatible mappings satisfying an implicit relation involving quadratic terms.…”

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.…”