G-β-Ψ contractive-type mappings and related fixed point theorems

Abstract

In this paper, we introduce the notion of generalized G-β-Ψ contractive mappings which is inspired by the concept of α-Ψ contractive mappings. We showed the existence and uniqueness of a fixed point for such mappings in the setting of complete G-metric spaces. The main results of this paper extend, generalize and improve some well-known results on the topic in the literature. We state some examples to illustrate our results. We consider also some applications to show the validity of our results. © 2013 Alghamdi and Karapinar;.