Abstract
Two common fixed point theorems for weakly compatible mappings satisfying contractive conditions of integral type in G -metric spaces are demonstrated. The results obtained in this paper generalize and differ from a few results in the literature and are used to prove the existence and uniqueness of common bounded and continuous solutions for certain functional equations and nonlinear Volterra integral equations. A nontrivial example is included.
Highlights
The Banach fixed point theorem which was first presented by Banach in 1922 is a significant result in fixed point theory
Because of its importance in proving the existence of solutions for functional equations, nonlinear Volterra integral equations and nonlinear integro-differential equations, this result has been extended in many different directions
In 2011, Aydi [1] proved a fixed point theorem for mappings satisfying a ðψ, φÞ-weakly contractive condition in G-metric spaces
Summary
The Banach fixed point theorem which was first presented by Banach in 1922 is a significant result in fixed point theory. In 2013, Gupta and Mani [21] obtained the existence and uniqueness of a fixed point for contractive mappings of an integral type in complete metric spaces by using iterative approximations. In 2011, Aydi [1] proved a fixed point theorem for mappings satisfying a ðψ, φÞ-weakly contractive condition in G-metric spaces. In 2012, Aydi [2] obtained the following common fixed point theorem for a pair of mappings involving a contractive condition of integral type in G-metric spaces. The objective of this paper is both to introduce two new classes of contractive mappings of integral type in the setting of G-metric spaces and to prove the existence and uniqueness of points of coincidence and common fixed points for these mappings.
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