Some Fixed Point Results on Complex Valued Sb-Metric Spaces

Abstract

More recently, the notion of a complex valued S b-metric space has been introduced and studied. In this paper, we investigate some basic properties of this new space. We study some fixed point results on a complete complex valued S b-metric space. A common fixed point theorem for two self-mappings on a complete complex valued S b-metric space is also given.

Bilateral-type solutions to the fixed-circle problem with rectified linear units application

“…were investigated in rectangular and quasi metric spaces (see [1,2]). Using known fixed-point techniques, some applications were presented to "Fixed-Circle Problem" on 2-cone Banach spaces, M b -metric spaces, rectangular M -metric spaces and parametric N b -metric spaces (see [6,13,19,29]). In some of the above studies, some open problems were left to improve fixed-circle problem.…”

Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application

“…In this section, we give an application to the fixed-circle problem which is a new geometric approach to fixedpoint theory raised by Özgür and Taş [8]. More recently, some different solutions of the problem have been investigated with various techniques on metric spaces or some generalized metric spaces (see [6], [7], [9], [10], [11], [12], [13], [18], [19], [20] and [21] for more details). In this context, we obtain new fixed-circle theorems on 2-cone normed spaces.…”

On unique and non-unique fixed point in parametric N b −metric spaces with application

“…These essentially centred around two components: (i) by changing the structure and (ii) by changing the conditions on the mapping under consideration. One such interesting structure, parametric N b -metric spaces is recently introduced by Tas and Özgür [21]. It generalizes the metric space (Fréchet [5]), b−metric space (Bakhtin [1] and Czerwik [4]), S−metric space (Sedghi et al [17]), S b −metric space (Souayah and Mlaiki [19] and Sedghi et al [16]), parametric S-metric space (Tas and Özgür [20]), A b -metric space (Ughade et al [30]) and so on.…”

“…Lemma 1 [21] In a parametric N b −metric space (X , N ), (i) N x,y,t ≤ bN y,x,t and N y,x,t ≤ bN x,y,t , (ii) N x,y,t ≤ b[(n − 1)N x,z,t + N y,z,t ] and N x,y,t ≤ b[(n − 1)N x,z,t + bN z,y,t ],…”