Fixed point results for GP(Λ,Θ) -contractive mappings

Abstract

In this paper, we introduce new notions of GP -metric space and GP (Λ,Θ) -contractive mapping and then prove some fixed point theorems for this class of mappings. Our results extend and generalized Banach contraction principle to GP -metric spaces. An example shows the usefulness of our results.

Gp-metric spaces-symmetric and asymmetric

“…The same holds for the proof of Theorem 3.1 of the paper [12] (see line 10 of page 9), and also for [19,Theorem 2.4] (see the end of the proof).…”

“…Following this definition, the authors in [3,4,6,19] obtained several fixed point results in G p -metric spaces. However, it is clear that the assumption (G p 2) of the previous definition readily implies that…”

Existence of fixed point for GP(Λ;Θ)-contractive mappings in GP-metric spaces

“…Following this idea, Aydi et al [4] established some fixed point results in GP-metric spaces. Other results in the setting of GP-metric spaces are available in [18], where the authors introduce the notion of GP (Λ,Θ) -contractive mappings and give some fixed point results for GP (Λ,Θ) -contractive mappings.…”