S-metric Space Research Articles

A Study on Soft S-Metric Spaces

The first aim of this paper is to define soft S-metric space and examine some of its properties. Later we define the concepts of soft continuous mapping, soft sequential continuous and investigate the relationship between them.

S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

Recently, some generalized metric spaces have been studied to obtain new fixed-point theorems. For example, the notion of S-metric space was introduced for this purpose. In this study, some fixed-point results are proved using different contractive conditions on S-metric spaces. Various techniques such as Hard-Rogers type contraction, Khan type contraction, Meir-Keeler-Khan type contraction are used in our theorems to be proved. These fixed-point results extend some known fixed-point theorems on S-metric spaces. Also, to illustrate obtained theoretical results, some examples are given using an S-metric which is not generated by any metric. As an application, a new fixed-circle result is presented using modified C-Khan type contraction on S-metric spaces.

Wardowski Type Contractions and the Fixed-Circle Problem on S-Metric Spaces

In this paper, we present new fixed-circle theorems for self-mappings on an S-metric space using some Wardowski type contractions, ψ-contractive, and weakly ψ-contractive self-mappings. The common property in all of the obtained theorems for Wardowski type contractions is that the self-mapping fixes both the circle and the disc with the center x0 and the radius r.

Common Fixed Points of Continuous Mappings on S-Metric Spaces

The aim of this paper is to obtain some common fixed point results on an S-metric space. For this purpose, we prove new generalized common fixed point theorems using the notions of weak commutation, compatibility, and orbital continuity for two and four continuous self-mappings. Our main results generalize the known common fixed point theorems on metric spaces.

The Picard Theorem on S-metric spaces

Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical “Picard Theorem”.

Common fixed point of four maps in S-metric spaces

In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works.

Fixed Point Theorems on Parametric A-metric Space

In this paper, we introduce the notion of parametric A-metric space as generalisation of parametric metric space and parametric S-metric space. Further we prove some fixed point theorem of expansive mapping in the setting of parametric A-metric space.

Cone S-Metric Space and Fixed Point Theorems of Contractive Mappings

Cone S-Metric Space and Fixed Point Theorems of Contractive Mappings

New contractive conditions of integral type on complete S-metric spaces

An S-metric space is a three-dimensional generalization of a metric space. In this paper our aim is to examine some fixed-point theorems using new contractive conditions of integral type on a complete S-metric space. We give some illustrative examples to verify the obtained results. Our findings generalize some fixed-point results on a complete metric space and on a complete S-metric space. An application to the Fredholm integral equation is also obtained.

Contraction principles in M_s-metric spaces

In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under different contraction principles.

A note on the paper "A fixed point theorems in Sb-metric spaces"

Very recently, N. Souayan and N. Mlaiki [Nazir Souayan and Nabil Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Comput. Sci. 16 (2016), 131-139] and S. Sedghi et al. [S. Sedghi, A. Gholidahneb, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixed point of four maps in Sb-metric spaces, to appear in J. Linear Topol. Algebra], introduced the concept of Sb-metric space as a generalization of S-metric space. In this paper, we modified the definition of Sb-metric introduced by Souayan and Mlaiki and prove some coupled common fixed point theorems in Sb-metric space. We also present an example to confirm our theoretical results.

Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25)

Recently, S-metric spaces are introduced as a generalization of metric spaces. In this paper, we consider the relationships between of an S-metric space and a metric space, and give an example of an S-metric which does not generate a metric. Then, we introduce new contractive mappings on S-metric spaces and investigate relationships among them by counterexamples. In addition, we obtain new fixed point theorems on S-metric spaces.

A Tripled Fixed Point Theorem in Partially Ordered Complete S-Metric Space

Sedghiet al.(Mat. Vesn. 64(3):258-266, 2012) introduced the notion of anS-metric as a generalized metric in 3-tuples S:X3→[0,∞), whereXis a nonempty set. In this paper we prove a tripled fixed point theorem for mapping having the mixed monotone property in partially ordered S-metric space. Our result generalize the result of Savitri and Nawneet Hooda (Int. J. Pure Appl. Sci. Technol. 20(1):111-116, 2014, On tripled fixed point theorem in partially ordered metric space) into the settings of S-metric space.

On a Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered S-Metric Space

In this paper we prove a fixed point theorem for mapping satisfying a contractive condition of rational type in partially ordered S-metric space. Our result generalize some existing results in the literature into settings of S-metric space.

A common unique fixed point theorem for expansive type mappings in S-metric spaces

In present paper, we prove a common unique fixed point theorem for expansive mappings in S-metric space which correspond to contractive mapping of theorem 1 in [10].