Some Common Fixed Point Theorems Satisfying Meir-Keeler Type Contractive Conditions

Abstract

In this article, we establish some common fixed point results for two pairs of compatible mappings satisfying Meir-Keeler type contractive conditions in metric space and dislocated metric space which extend and improve some similar fixed point results in the literature.

A Meir-Keeler Type Common Fixed Point Result in Dislocated Metric Space

“…Our result generalizes the Meir-Keeler [11] fixed point theorem in dislocated metric space and extends the results of Pant and Jha [13], Bouhadjera and Djoudi [2], Jha, Pant and Singh [4] and Panthi [14].…”

“…A d-metric space (X, d) is called complete if every Cauchy sequence in it is convergent with respect to d. Lemma 1. [14] Let (X, d) be a dislocated metric space. Let A, B, S, T : X → X be mappings satisfying the conditions A(X) ⊆ T (X) and B(X) ⊆ S(X)…”