S-metric Space Research Articles

Fixed Points From Kannan Type S-Coupled Cyclic Mapping In Complete S-Metric Space

Fixed Points From Kannan Type S-Coupled Cyclic Mapping In Complete S-Metric Space

A COMPLETION THEOREM FOR COMPLEX VALUED S-METRIC SPACE

Any complex valued S-metric space where each Cauchy sequence converges to a point in this space is said to be complete. However, there are complex valued S-metric spaces that are incomplete but can be completed. A completion of a complex valued S-metric space ( is defined as a complete complex valued S-metric space with an isometry such that is dense in In this paper, we prove the existence of a completion for a complex valued S-metric space. The completion is constructed using the quotient space of Cauchy sequence equivalence classes within a complex valued S-metric space. This construction ensures that the new space preserves the essential properties of the original S-metric space while being completeness. Furthermore, isometry and denseness are redefined regarding a complex valued S-metric space, generalizing those established in a complex valued metric space. In addition, an example is also presented to illustrate the concept, demonstrating how to find a unique completion of a complex valued S-metric space.

Some Fixed Point Theorems in Convex S-Metric Space

In this paper, we introduce convex S-metric space. We also establish and prove some fixed point theorems for self-mappings satisfying certain contraction principles on a complete convex S-metric space. Some examples are presented to validate the originality and applicability of our results. Finally, we improve, generalize and extend some recent results.

GENERALIZATION OF BANACH FIXED POINT THEOREM FOR T-ORBITALLY COMPLETE DISLOCATED METRIC SPACE

Generalization of Banach Fixed Point Theorem for different metric spaces like dislocated metric space, dislocated quasi metric space, b-metric space and S-metric space etc was studied by several authors using different conditions on self-mapping. Dolhare and Nalawade studied the generalization in -orbitally complete metric space. In this research article, we have proved two new results of the existence and uniqueness of fixed point for selfmapping in -orbitally complete dislocated metric space by the rationalization condition on . Also, we have proved consequences of our main results.

Type (K) Compatible Mappings and Common Fixed Points in Complete Cone S-metric Spaces

Objective: This research work is an attempt to explore common fixed points for four self-maps that are pairwise type ( ) compatible in a complete cone -metric space. Method: We have applied a contractive condition together with a weaker condition, compatible of type (K) to establish fixed points that are common for four self-maps. Findings: Some already existing results in the literature have been generalized, expanded upon, and new fixed point results have been obtained in cone S-metric spaces. To back up our conclusions, a suitable example is provided. Novelty: By adopting an appropriate contractive condition, we have proven the existence of a unique common fixed point for four maps in a cone -metric space, despite the weak compatible condition. MSC 2020: 47H10, 54H25. Keywords: Normal Cone, Partial Ordering, Cone S-metric Space, Compatible Mappings of Type (K), Common Fixed Point

S-Pata-type contraction: a new approach to fixed-point theory with an application

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions.

Some fixed point results of F-contraction in parametric S-metric spaces

In this paper, we introduce the concept of F-contractions in parametric S-metric space. Further, we prove a unique fixed point theorem in parametric S-metric space. Another result is also obtained as corollary.

O nekim rezultatima fiksne tačke za ekspanzivna preslikavanja u S-metričkim prostorima

Introduction/purpose: The aim of this paper is to establish some existence results of a fixed point for a class of expansive mappings defined on a complete S-metric space. Methods: An iteration scheme was used. Results: Some existing results of mappings satisfying contractive conditions are expanded to expansive ones, providing a new condition expressed in one variable under which the existence of a fixed point holds. Conclusions: This work provides new tools to fixed point theory together with their applications.

Some Fixed-Point Results in Extended S-Metric Space of Type (α,β)

In this paper, we introduce the notion of extended S-metric space of type (α,β). This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition of the S-metric space definition. Accordingly, we prove some fixed-point results and give some examples to illustrate the validity of our work, along with giving an application of the Fredholm integral equation.

GENERALIZED FIXED POINT RESULT OF BANACH AND KANNAN TYPE IN S-MENGER SPACES

S-metric space is a relatively new concept in the literature and currently there is much attention being given to the generalization of S-metric spaces and fixed point theory in these spaces. Recently, the concept of S-Menger spaces was introduced in the literature as a generalization of both S-metric spaces and Menger spaces. Combinations of Banach and Kannan type contractions are very much important to find fixed point results and there are very few works on S-metric spaces that includes both of these type contractions. In this paper, we present a fixed point result in S-Menger spaces that includes both Banach type contractions and Kannan type contractions. We have also deduced some corollaries from our result and provided examples to validate our work.

Some Invariant Point Results Using Simulation Function

Through this article, we establish an invariant point theorem by defining generalized Zs-contractions in relation to the simulation function in S-metric space. In this article, we generalized the results of Nihal Tas, Nihal Yilmaz Ozgur and N.Mlaiki. In addition to that, we bestow an example which supports our results.

Common Fixed Point Theorem for Four Weakly Compatible Self Maps on a Complete S-Metric Space

In the present paper, we establish a common fixed point theorem for four weakly compatible self maps of a S-metric space.

A Focus on Types of Compatible Mappings in \(S\)-metric Space

In this article, we study unique common fixed point theorems for four self mappings in S-metric space using generalized concepts of compatible mappings such as compatible mappings of type (A), type (B) and type (C). Our results are generalizing the theorems proved by Sedghi et al. (Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018), 137 – 143) in metric space.

Common Fixed-point Theorem for Four Weakly Compatible Self-maps Satisfying (E.A) — Property on a Complete S-metric Space

Objectives: To establish a fixed-point theorem on a complete S -metric space. Methods: By using (E.A)-property of self-maps and applying the concept of strong comparison function. Findings: Obtained a unique common fixed-point theorem for four self-maps of a complete S-metric space and validated it with a suitable example. Novelty: By utilizing weak compatibility together with (E.A)- property, a unique common fixed point is obtained for four self-maps which is more robust generalization of the existing theorems in the literature which are proved by using common limit range property. Mathematics Subject Classification: 47H10, 54H25 Keywords: (EA)-property; Weak compatibility; Comparison function; Fixed point; S - metric space

A Common Fixed-point Theorem of Mappings on S-metric Spaces

Fixed Point Theory is developed during the years by generalizing various types of contractions or changing the axioms of metric spaces. The S-metric spaces extend the concept of metric spaces since the determination of axioms of S-metric are more general. In this paper, we prove a common fixed-point theorem of two mappings in S-metric space. The theorem uses an implicit contractive condition, based on functions of class F6. With the change of the form of the functions of class F6 , we obtain different results for common fixed points of two functions.

A Fixed Point Result with (CLR) Property in S-Metric Spaces

Objective : The present paper is an attempt to improve results on fixed point theorems for four pairwise occasionally weakly compatible (owc) mappings in S-metric spaces. Method: We have applied quadratic inequality to prove certain fixed-point results for four pairwise owc mappings under weaker conditions using (CLR) property. Findings: We have generalized and expanded some already existing results in the literature and new results are obtained that generated the common fixed points in S-metric spaces. Befitting examples are given to support our findings. Novelty: Existence and uniqueness of fixed points in S-metric spaces are established by using (CLRFG) property even in the absence of containment conditions. 2010 Mathematics Subject Classification: 47H10, 54H25 Keywords: Smetric Space; Coincidence Point; Common Fixed Point; Occasional Weak Compatibility; (CLR) Property

On a coupled fixed point theorem for a mapping satisfying a contraction of rational type in partially ordered S-metric space

In this paper, the concept of S-metric is used as a generalizion of the ordinary metric space to obtain a coupled fixed point result for a mapping satisfying a contraction of rational type in partially ordered S-metric space. Since such results has already been proved in ordinary metric space, similar procedure was followed in stating and proving our result in the setting of S-metric space. The result presented here modify and generalize the existing result of Circ et al (2012) which was stated in partially ordered metric space.

New fixed-disc results via bilateral type contractions on S-metric spaces

There are some examples of self-mappings which does not satisfy the Banach contractive condition and have a unique fixed point or more than one fixed point. In this case, metric fixed-point theory has been extensively generalized using some techniques. One of these techniques is to generalize the used contractive conditions such as the Jaggi type contractive condition, the Dass-Gupta type contractive condition etc. Another technique is to generalize the used metric spaces such as a b-metric space, an S-metric space etc. The last technique is to investigate geometric properties of the fixed-point set of a given self-mapping such as fixed circle, fixed disc etc. For this purpose, “fixed-circle problem” has been studied with various techniques as a geometrical generalization of the metric fixed-point theory. This problem was also considered as “fixed-figure problem”. Some solutions to these recent problems were obtained using different contractions both a metric space and a generalized metric space. The main purpose of this paper is to prove some fixed-disc theorems on an S-metric space. To do this, we modify the known contractive conditions. Also, the obtained new theorems are supported by some illustrative examples.

Outcomes of Common Fixed Point Theorems in S-metric Space

In the present paper, we establish the existence of two unique common fixed point theorems with a new contractive condition for four self-mappings in the S-metric space. First, we establish a common fixed-point theorem by using weaker conditions such as compatible mappings of type-(E) and subsequentially continuous mappings. Further, in the next theorem, we use another set of weaker conditions like sub-compatible and sub-sequentially continuous mappings, which are weaker than occasionally weak compatible mappings. Moreover, it is observed that the mappings in these two theorems are sub-sequentially continuous, but these mappings are neither continuous nor reciprocally continuous mappings. These two results will extend and generalize the existing results of [7] and [9] in the S-metric space. Furthermore, we also provide some suitable examples to justify our outcomes.

Fixed points of modified F-contractions in S-metric spaces

In this paper, we introduce a modified F-contraction in S-metric space. This modified form of F-contraction is via α-admissible mapping and we use it to examine the existence of fixed points in S-metric spaces. Sufficient examples are also given to examine the validity of the results obtained.