A New Generalization of M-Metric Space With Some Fixed Point Theorems

Abstract

In this paper, we introduce a new sequential space as a generalization of M − metricspaces and M b − metric spaces. In this generalized space we define two contractive mappings namely m − contraction and m − quasi-contraction and prove some fixed point theorems for such type of mappings. Several illustrative examples have been presented in strengthening the hypothesis of our theorems.

Controlled v-generalized metric type space and some fixed point theorems with application

“…One of those is the concept of b-metric spaces which was introduced by Czerwik [6] in 1993. The concepts of metric and b-metric structures have been generalized in many ways (see [3,4,10,15,16,17,18,19,20,21,22,23]). Branciari [5] presented rectangular metric space in 2000, another such generalized metric structure, where the triangle inequality had been replaced by a so-called quadrilateral or rectangular inequality.…”