New Contractive Conditions for Maps in G-metric Type Spaces

Abstract

In this article, we introduce a new type of contractive self maps defined in G-metric type spaces and prove a common fixed point theorem. We establish that under the convergence of a certain series, a family of self maps have a common fixed point.

Related G-metrics and Fixed Points

“…Finally, we point out that many results about the fixed point theory in G-metric spaces can be read in [1][2][3][4][5][6][7][8][9][11][12][13][14][15]].…”

Common Fixed Points via λ-Sequences in G-Metric Spaces

“…We also make use of a special class of homogeneous functions. Recent and similar work can also be read in [2,3,6,7].…”

“…In recent years, several authors have obtained fixed point and common fixed point results for various classes of mappings in the setting of many generalized metric spaces. One of them, the -metric space, is our focus in this paper, and fixed point results, in this setting, presented by authors like Abbas et al [1], Gaba [2,3], Mustafa and Sims [4], Sihag et al [5], and many more, are enlightening on the subject. Moreover, in [6], we introduced the concept of -sequence which extended the idea of -series proposed by Sihag et al in [5].…”