A common fixed point theorem for a pair of generalized contraction mappings with applications

Abstract

In this article, we introduce abscissa dominating function F: [0;∞)2 → ℝ and define a generalized (α, F;ψ, φ) contraction mapping which retrieves Banach's contraction, Geraghty type contraction and weak contraction as particular cases. We establish a common fixed points theorem for a pair of generalized (α, F;ψ, φ)-contraction mappings in complete partial metric spaces and apply this theorem to show the existence of solution of system of integral equations. This result and its consequences generalize many existing results both in partial metric spaces and metric spaces. We give examples to illustrate our results and to express the usefulness of these results in the literature.