Contractions In Fuzzy Metric Spaces Research Articles

Convergence results based on graph-Reich contraction in fuzzy metric spaces with application

This article introduces a novel class of Reich-type contractions that meet the graph preservation criteria in the context of complete fuzzy metric spaces. The provided contraction condition is satisfied through various forms of contractive mappings via directed graphs in the literature. Our key result is the natural extension of fuzzy metric spaces to fuzzy metrics enriched with a graph, which adds the understanding of fixed points in metric spaces within the realm of graph structure. The findings are further supported by examples and applications.

Fixed Point Theorem for Fuzzy B-type Contractions in Fuzzy Metric Spaces

Recently, in 2021, Bijender et al. proposed the establishment of -contraction. Such sort of contraction is a genuine generalization of the standard contraction in the study of metric fixed point theory. The aim of the present study is the establishment of the novel concept of the fuzzy B-type contraction in the settings of fuzzy metric space and such contractions are also used to establish a few fixed point theorems.

κG‐Contractive Mappings in Fuzzy Metric Spaces

This article is concerned with a class of contractions in the framework of a fuzzy metric space endowed with a graph. The main results obtained not only broaden but also generalize a number of relevant results in the literature. Particularly, we get some results for cyclic contractions in fuzzy metric spaces. We also consider an integral equation.

A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions.

Some fixed point theorems for $$S_F$$ S F -contraction in complete fuzzy metric spaces

In this paper, we prove some fixed point theorems by introducing a new F-contraction namely $$S_F$$ -contraction in fuzzy metric spaces by combining the idea of Wardowski’s (Fixed Point Theory Appl 2012, Article ID 94, 2012) and Secelean’s (Fixed Point Theory Appl 2013, Article ID 277, 2013) contractions in metric spaces and Grabiec’s (Fuzzy Sets Syst 125, 385–389, 1988) contraction in fuzzy metric spaces. An example is also given to support the results proved herein.

Fixed point results for $mathcal{H}$-contractions in fuzzy metric spaces via admissible

Fixed point results for $mathcal{H}$-contractions in fuzzy metric spaces via admissible

Fixed point results for modified various contractions in fuzzy metric spaces via α-admissible

In this paper, we prove the existence of a fixed point for some new classes of ?-admissible contraction mappings in fuzzy metric spaces. Our results generalize and extend some well-known results on the topic in the literature. Moreover, we present some examples to illustrate the usability of the obtained results.

Some Theorems about(ψ,φ,ϵ,λ)-Contraction in Fuzzy Metric Spaces

We previously proved a number of fixed point theorems for some kinds of contractions likebn-contraction andφ-Hcontraction in fuzzy metric spaces. In this paper, we discuss the problem of existence of fixed point for(ψ,φ,ϵ,λ)-contraction in fuzzy metric spaces in sense of George and Veeramani.

Some remarks on fuzzy contractive mappings

Recently a new concept of fuzzy contraction in fuzzy metric spaces in the sense of George and Veeramani (Wardowski, 2013 [5]) has been introduced. Here we provide some comments to this paper.

Fixed point theory for cyclic $varphi$-contractions in fuzzy metric spaces

In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inconnection with the fixed point are given.

(ψ,α,β)-weak contraction in fuzzy metric spaces

The aim of this paper is to establish some new common fixed point theorems for mappings employing -weak contraction in fuzzy metric spaces. Our results generalize and improve various well known comparable results

Answers to some open questions on fuzzy [formula omitted]-contractions in fuzzy metric spaces

In this paper, we answer two open questions posed by Mihet [Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Syst. 159 (2008) 739–744] and Gregori et al. [Some questions in fuzzy metric spaces, Fuzzy Sets Syst. 204 (2012) 71–85]. We give a positive answer for the question of Mihet by means of Theorem 1 and a negative answer for the question of Gregori et al. by means of Example 1.

Fixed Point Theory for Cyclic Weak $\phi-$contraction in Fuzzy Metric Spaces

In this paper, we introduce cyclic weak $\phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.

Note on “Coupled fixed point theorems for contractions in fuzzy metric spaces”

In the paper “Coupled fixed point theorems for contractions in fuzzy metric spaces” by Sedghi et al. [S. Sedghi, I. Altun, N. Shobec, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72 (2010) 1298–1304], a coupled common fixed point result was presented. However, our purpose is to show that this result and its proof are false. We give a counterexample and also explain how to correct this result. As a modification, we state and prove a coupled fixed point theorem under some hypotheses of fuzzy metric and t -norm.

A class of contractions in fuzzy metric spaces

Using the notion of geometrically convergent t-norms, a fixed point theorem in fuzzy metric spaces in the sense of Kramosil and Michalek for a class of contractions, larger than the class of ( ε , λ ) -contraction mappings, has been proved.

Coupled fixed point theorems for contractions in fuzzy metric spaces

In the present work, we prove a coupled fixed point theorem for contractive mappings in complete fuzzy metric spaces.