A Fixed Point in Partial Sb-Metric Spaces

Abstract

In this paper, we introduce an interesting extention of the partial bmetric spaces called partial S b -metric spaces, and we show the existence of fixed point for a self mapping defined on such spaces.

S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

“…We expect that this study will help to generate some new researches and applications about fixed-point or fixed-circle theorems on different generalized metric spaces. For example, it is possible to study similar results on an S b -metric space (see [18] and [19] for more details about S b -metric spaces).…”

Fixed point theorems in partial $S_b$-metric spaces

“…For example, S. G. Matthews [12] defined partial metric space, Bakhtin [4] introduced bmetric spaces, S. Shukla [15] Partial-b metric spaces and generalization of many results related to fixed point theories have been studied in those spaces( [3], [16], [17]). Nizar Souayah [9] introduced partial S b metric space as an extension of partial b-metric spaces and studied few fixed point theorems. This paper is a modification of [9] as well as an extension of the study of partial S b -metric spaces.…”

“…Nizar Souayah [9] introduced partial S b metric space as an extension of partial b-metric spaces and studied few fixed point theorems. This paper is a modification of [9] as well as an extension of the study of partial S b -metric spaces. Let's provide few definitions as ready references, Definition 1.1.…”

On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

“…The concept of the b-metric space has inspired many researchers to investigate fixed-point theorems under different hypotheses [13][14][15][16]. Also, several generalizations of this metric space have been developed [17][18][19][20][21][22]. In 2017, Kamran et al [23] generalized the concept of the b-metric space by replacing on the triangle inequality the constant s by a function s(x 1 , x 2 ), then they obtained an extended b-metric space defined as follows.…”