Fixed Point Results for <i>g<sup>m</Sup>< Contractive and <i>g</I>-(α, Ψ)-Meir Contractive Mappings

Abstract

In this paper, first we introduce the notion of a G(m)-Meir-Keeler contractive mapping and establish some fixed point theorems for the G(m)-Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a G(c)(m)-Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(alpha, psi)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.