DOI: 10.24193/fpt-ro.2025.2.14

Authors: Mohamed Jleli, Cristina Maria Păcurar and Bessem Samet

Abstract: We are concerned with the study of fixed points for mappings T : X → X, where (X,G) is a G-metric space in the sense of Mustafa and Sims. After the publication of the paper [Journal of Nonlinear and Convex Analysis, 7(2) (2006) 289-297] by Mustafa and Sims, a great interest was devoted to the study of fixed points in G-metric spaces. In 2012, the first and third authors observed that several fixed point theorems established in G-metric spaces are immediate consequences of known fixed point theorems in standard metric spaces. This observation demotivated the investigation of fixed points in G-metric spaces. In this paper, we open new directions in fixed point theory in G-metric spaces. Namely, we establish new versions of the Banach, Kannan and Reich fixed point theorems in G-metric spaces. We point out that the approach used by the first and third authors [Fixed Point Theory Appl. 2012 (2012) 1-7] is inapplicable in the present study. We also provide some interesting applications related to mappings contracting perimeters of triangles.

Key Words and Phrases: Fixed point, G-metric, mappings contracting perimeters of triangles.

2010 Mathematics Subject Classification: 47H10, 54E50, 47S20.

Published on-line: May 1st, 2025.

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