Structure for $g$-Metric Spaces and Related Fixed Point Theorems

Abstract

In this paper, we propose a generalized notion of a distance function, called a g-metric.The g-metric with degree n is a distance of n + 1 points, generalizing the ordinary distance between two points and G-metric between three points. Indeed, it is shown that the g-metric with degree 1 (resp. degree 2) is equivalent to the ordinary metric (resp. the G-metric). Fundamental properties and several examples for the g-metric are also given. Moreover, topological properties on the g-metric space including the convergence of sequences and the continuity of mappings on the g-metric space are studied. Finally, we generalize some well-known fixed point theorems including Banach contraction mapping principle and Ćirić fixed point theorem in the g-metric space.

Generalized multiplicative nonlinear elastic matching distance measure and fixed point approximation

“…For more relevant literature, readers are advised to study Nagpal et al, 15 wherein various examples have already been discussed. Also, Choi et al 16 established a more relevant instance of a generalized metric space g-metric in more generalized way. For more information, see previous studies 11, [16][17][18][19][20] and references therein.…”

“…Also, Choi et al 16 established a more relevant instance of a generalized metric space g-metric in more generalized way. For more information, see previous studies 11, [16][17][18][19][20] and references therein.…”