Related fixed point results for cyclic contractions on G-metric spaces and application

Abstract

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

Fixed Point Theorems in General Metric Space with an Application

“…As known, Banach, is the first to do this in his Ph.D. thesis (1) . For many other results in this branch see, (8)(9)(10)(11)(12)(13)(14)(15). It is worth noting to citation a new Al-Bundy's results (16)about constructing a fractal in − metric spaces.…”

New Fixed Point Results for Generalized Θ-Contraction in Extended 𝐆𝐛-Metric Spaces with an Application

“…Over the past few centuries, fixed point theory has been one of the increasingly significant fields of research in nonlinear functional analysis. Mustafa and Sims [1] initiated the idea of G-metric spaces, which is subsequently studied and proposed to acquire various types of fixed point theorems, see [2][3][4][5][6][7]. Based on the ideas of G-metric spaces (GMS) and b-metric spaces, Aghajani et al examined the conception of Gbmetric spaces (GbMS).…”

Two New Geraghty Type Contractions in Gb-Metric Spaces

“…The notion of -metric spaces was introduced by Mustafa and Sims [5] as a generalization of metric spaces. Thereafter, -metric spaces have been studied and applied to obtain different kinds of fixed point theorems, see [6][7][8][9][10][11][12]. Aghajani et al [13] introduced the notion of -metric spaces based on -metric spaces and -metric spaces introduced by Bakhtin in [14].…”