A fixed point theorem in S_b-metric spaces

Abstract

In this paper, we introduce an interesting extension of the S-metric spaces called S b -metric spaces, in which we show the existence of fixed point for a self mapping defined on such spaces. We also prove some results on the topology of the S b -metric spaces.

Extended Partial Sb-Metric Spaces

“…Fixed point theory has become the focus of many researchers lately due its applications in many fields see [1][2][3][4][5][6][7][8][9][10][11][12]). The concept of b-metric space was introduced by Bakhtin [13], which is a generalization of metric spaces.…”

Some Common Coupled Fixed Point Theorems in Sb-Metric Spaces

“…Very recently, Souayah and Mlaiki [12] introduced the concept of S b -metric space as a generalization of the b-metric space and proved some fixed point results. R Sedghi et al [13] also introduced the concept of S b -metric space and their definition of S b -metric space is different from the definition of S b -metric space given by Souayah and Mlaiki [12].…”

“…Very recently, Souayah and Mlaiki [12] introduced the concept of S b -metric space as a generalization of the b-metric space and proved some fixed point results. R Sedghi et al [13] also introduced the concept of S b -metric space and their definition of S b -metric space is different from the definition of S b -metric space given by Souayah and Mlaiki [12]. Sedghi et al [13] defined the definition of S b -metric space without condition (ii) of definition (1) whereas Souayah and Mlaiki [12] considered condition (ii) of definition (1) to be a part of the definition.…”

“…R Sedghi et al [13] also introduced the concept of S b -metric space and their definition of S b -metric space is different from the definition of S b -metric space given by Souayah and Mlaiki [12]. Sedghi et al [13] defined the definition of S b -metric space without condition (ii) of definition (1) whereas Souayah and Mlaiki [12] considered condition (ii) of definition (1) to be a part of the definition. Y. Rohen et al [14] also proved some coupled fixed point theorem in S b -metric space.…”

“…(i) S b (x, y, z) = 0 if and only if x = y = z, (ii) S b (x, x, y) = S b (y, y, x) for all x, y ∈ X, 12]). Note that the class of S b -metric spaces is larger than the class of S-metric spaces.…”