Mappings In Fuzzy Metric Spaces Research Articles

Common fixed point theorems for ψ-weakly commuting maps in fuzzy metric space

In this paper we obtain some fixed point and common fixed point theorems for mappings satisfying general contractivity condition in the setting of fuzzy metric spaces. Some recent results are also derived as special cases.

Common fixed point theorems for hybrid pairs of maps in fuzzy metric spaces

The purpose of this paper is to introduce the notion of common limit range property (CLR property) for two hybrid pairs of mappings in fuzzy metric spaces, and we prove common fixed point theorems using (CLR) property for these mappings with implicit relation. Our results extend some known results to multi-valued arena. Also, we prove common fixed point theorem in fuzzy metric spaces satisfying an integral type.

Existence and uniqueness of a common fixed point under a limit contractive condition

Abstract In this paper, utilizing the notion of common limit range property for two pairs of self mappings, we prove common fixed point theorems in fuzzy metric spaces under a limit contractive condition, which improve and extend the results of Zhu et al. [Common fixed point theorems of new contractive conditions in fuzzy metric spaces, J. Appl. Math. 2013:145190, 2013]. We also give some examples to demonstrate the validity of the hypotheses of our results. As an application to our main result, we obtain a fixed point theorem for four finite families of self mappings in fuzzy metric space. MSC: 47H10, 54H25.

Fixed points of fuzzy contractive set-valued mappings and fuzzy metric completeness

In this paper, we introduce a new fuzzy contraction via a new concept of the fuzzy sets called fw-distances initiated in the paper, which is a generalization of a fuzzy contractive mapping initiated in the article (Fuzzy Sets Syst. 159:739-744, 2008). A fixed point theorem is established by using this type of contraction of set-valued mappings in fuzzy metric spaces which are complete in the sense of George and Veeramani. As an application of our results, we give characterizations of fuzzy metric completeness. The results are supported by examples.

Common coupled fixed point theorems for weakly compatible mappings in fuzzy metric spaces

In this paper, we prove a common fixed point theorem for weakly compatible mappings under ϕ-contractive conditions in fuzzy metric spaces. We also give an example to illustrate the theorem. The result is a genuine generalization of the corresponding result of Hu (Fixed Point Theory Appl. 2011:363716, 2011, doi:10.1155/2011/363716). We also indicate a minor mistake in Hu (Fixed Point Theory Appl. 2011:363716, 2011, doi:10.1155/2011/363716).

Common fixed point theorems for nonlinear contractive mappings in fuzzy metric spaces

In this paper, we prove several common fixed point theorems for nonlinear mappings with a function ϕ in fuzzy metric spaces. In these fixed point theorems, very simple conditions are imposed on the function ϕ. Our results improve some recent ones in the literature. Finally, an example is presented to illustrate the main result of this paper.

Fixed point theorems for cyclic contraction mappings in fuzzy metric spaces

In the present paper, an extension of the Edelstein contraction theorem for cyclic contractions in a fuzzy metric space is established, which also can be considered as a generalization of the fuzzy Edelstein contraction theorem introduced by Grabiec. Additionally, we extend a fixed point theorem in G-complete fuzzy metric spaces given by Shen et al. to M-complete fuzzy metric spaces. Meantime, two examples are constructed to illustrate the corresponding results, respectively.

Unified fixed point theorems in fuzzy metric spaces via common limit range property

The object of this paper is to utilize the notion of common limit range property to prove unified fixed point theorems for weakly compatible mappings in fuzzy metric spaces satisfying an implicit relation due to Rao et al. (Hacet. J. Math. Stat. 37(2):97-106, 2008). Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. As an application to our main result, we prove an integral type fixed point theorem in fuzzy metric space.MSC:54H25, 47H10.

FIXED POINT THEOREM IN FUZZY METRIC SPACE FOR NON COMPATIBLE MAPS

In this paper ,the concept of non compatible maps in fuzzy metric space has been applied to prove common fixed point theorem . A fixed point theorem for six self maps has been established using the concept of non compat- ible maps. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm.

Tripled fixed point theorem in fuzzy metric spaces and applications

Abstract In this paper we prove an existence and uniqueness theorem for contractive type mappings in fuzzy metric spaces. In order to do that, we consider a slight modification of the concept of a tripled fixed point introduced by Berinde et al. (Nonlinear Anal. TMA 74:4889-4897, 2011) for nonlinear mappings. Additionally, we obtain some fixed point theorems for metric spaces. These results generalize, extend and unify several classical and very recent related results in literature. For instance, we obtain an extension of Theorem 4.1 in (Zhu and Xiao in Nonlinear Anal. TMA 74:5475-5479, 2011) and a version in non-partially ordered sets of Theorem 2.2 in (Bhaskar and Lakshmikantham in Nonlinear Anal. TMA 65:1379-1393, 2006). As application, we solve a kind of Lipschitzian systems in three variables and an integral system. Finally, examples to support our results are also given.

Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces

Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces

Tripled fixed points for compatible mappings in fuzzy metric spaces

In this paper, we will introduce compatibility for triplet in fuzzy metric spaces. Our result includes modified definition of tripled fixed point and generalizes recent results of Roldan et al. about tripled fixed point in fuzzy metric spaces. At the end of the paper, we will provide an example in support of our result.

Weakly Compatible Mappings along with $CLR_{S}$ property in Fuzzy Metric Spaces

The aim of this work is to use newly introduced property, which is so called ”common limit in the range (CLRS)” for four self-mappings, and prove some theorems which satisfy this property. Moreover, we establish some new existence of a common fixed point theorem for generalized contractive mappings in fuzzy metric spaces by using this new property and give some examples to support our results. Ours results does not require condition of closeness of range and so our theorems generalize, unify, and extend many results in literature. Our results improve and extend the results of Cho et al. [4], Pathak et al. [20] and Imdad et. al.[10] besides several known results.

Erratum to: "Sub compatible and sub sequentially continuous maps in fuzzy metric spaces" by M. Alamgir Khan and Sumitra, Applied Mathematical Sciences, Vol. 5, 2011, no. 29, 1421-1430

Erratum to: "Sub compatible and sub sequentially continuous maps in fuzzy metric spaces" by M. Alamgir Khan and Sumitra, Applied Mathematical Sciences, Vol. 5, 2011, no. 29, 1421-1430

Common Fixed Point Theorem for Semi-Compatible and Sub Compatible Maps in Fuzzy Metric Space

In this paper we give common fixed point theorem in fuzzy metric space using concept of semi compatible and sub compatible satisfying implicit relation for two pair of self maps. −−−−−−−−−−−−−−−−−−−−−−−−−−−−

Fixed Point Theorem in Fuzzy Metric Spaces Satisfying E.A Property

The present paper is an attempt to prove common fixed point theorem for six mappings in fuzzy metric spaces. Our main result extends and improves the strict contractive conditions on fuzzy metric spaces and establishes the existence of common fixed points for six mappings under general contractive condition of integral type by using E.A property. The concept of weak compatible mappings is also used to prove the desired result.

Fixed Point Theorems For Self Mappings In Fuzzy Metric Space

Fixed Point Theorems For Self Mappings In Fuzzy Metric Space

Common Fixed Point Theorems for Sequences of Mappings in Fuzzy Metric Spaces

The purpose of this paper is to study common xed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric spaces. without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorem, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy metric spaces. We show that completeness of the whole space is not necessary for the existence and uniqueness of common xed point. Also, we prove a common xed point theorem for two self mappings and two sequences set-valued mappings by the same weaker conditions. Our results generalize, extend and improve the corresponding results given by many authors.

Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to our results, we obtain the corresponding xed pointtheorems in fuzzy metric spaces. Our results improve and extend the results ofKohli and Vashistha [Common xed point theorems in probabilistic metric spaces,Acta Math. Hungar. 115(1-2) (2007), 37-47], Vasuki [Common xed points forR-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math.30 (1999), 419{423], Chugh and Kumar [Common xed point theorem in fuzzymetric spaces, Bull. Cal. Math. Soc. 94 (2002), 17{22] and Imdad and Ali [Somecommon xed point theorems in fuzzy metric spaces, Math. Commun. 11(2)(2006), 153-163].

Applications of E.A. Property to Rational Inequality in Fuzzy Metric Spaces

In this paper common fixed point theorems using E.A. property via rational inequality for the class of four non compatible mappings in fuzzy metric spaces are proved. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm.