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

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

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

In 2002, Aamri and El-Moutawakil [2] defined the notion of (E.A) property for self mappings which contained the class of non-compatible mappings in metric spaces. It was pointed out that (E.A) property allows replacing the com- pleteness requirement of the space with a more natural condition of closedness of the range as well as relaxes the compleness of the whole space, continuity of one or more mappings and containment of the range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. Many authors have proved common fixed point theorems in fuzzy metric spaces for different contractive conditions. For details, we refer to [5, 10, 11, 15– 17, 20, 24–26, 29, 30, 32–34, 36, 37]. Recently, Sintunavarat and Kumam [35] defined the notion of (CLRg) property in fuzzy metric spaces and improved the results of Mihet¸ [18] without any requirement of the closedness of the subspace. In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings by using (CLRg) property in fuzzy metric space. We also present a common fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting due to Imdad, Ali and Tanveer [12]. Our results improve the results of Sedghi, Shobe and Aliouche [31].
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Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.
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Common Fixed Point Theorems for Weakly Compatible Mappings using Common Property (E.A) in Intuitionistic Fuzzy Metric Space of Integral Type

Common Fixed Point Theorems for Weakly Compatible Mappings using Common Property (E.A) in Intuitionistic Fuzzy Metric Space of Integral Type

11. S.Manro, S.S.Bhatia and S.Kumar, Common fixed point theorems for weakly compatible maps satisfying common (E.A) property in intuitionistic fuzzy metric spaces using implicit relation, Journal of Advanced Studies in Topology, 3(2) (2012) 38-44.

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Some common fixed point theorems for various types of compatible mappings in intuitionistic fuzzy metric spaces

Some common fixed point theorems for various types of compatible mappings in intuitionistic fuzzy metric spaces

the help of continuous t- norm and continuous t- conorm, as a generalization of fuzzy metric space due to George and Veeramani [6]. Alaca et al.[3] defined the notion of intuitionistic fuzzy metric spaces and proved common fixed point theorems. Turkoglu et al. [14] first formulate the definition of weakly commuting

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

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

In 2008, Al-Thagafi and Shahzad [Generalized I-nonexpansive selfmaps and invariant approxima- tions, Acta Math. Sinica 24(5) (2008), 867–876] introduced the notion of occasionally weakly com- patible mappings (shortly owc maps) which is more general than all the commutativity concepts. In the present paper, we prove common fixed point theorems for families of owc maps in Menger spaces. As applications to our results, we obtain the corresponding fixed point theorems in fuzzy metric spaces. Our results improve and extend the results of Kohli and Vashistha [Common fixed point theorems in probabilistic metric spaces, Acta Math. Hungar. 115(1-2) (2007), 37-47], Vasuki [Common fixed points for R-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math. 30 (1999), 419–423], Chugh and Kumar [Common fixed point theorem in fuzzy metric spaces, Bull. Cal. Math. Soc. 94 (2002), 17–22] and Imdad and Ali [Some common fixed point theorems in fuzzy metric spaces, Math. Commun. 11(2) (2006), 153-163].
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5. Common fixed point Theorems for non compatible mappings in fuzzy  metric spaces

5. Common fixed point Theorems for non compatible mappings in fuzzy metric spaces

The evolution of fuzzy mathematics commenced with the introduction of the notion of fuzzy sets by Zadeh [18] in 1965, as a new way to represent the vague- ness in every day life. In mathematical programming, problems are expressed as optimizing some goal function given certain constraints, and there are real life problems that consider multiple objectives. Generally, it is very difficult to get a feasible solution that brings us to the optimum of all objective functions. A possible method of resolution, that is quite useful, is the one using fuzzy sets [17]. The concept of fuzzy metric space has been introduced and generalized by many ways ( [4], [7] ). George and Veeramani ( [5] ) modified the concept of fuzzy metric space introduced by Kramosil and Michalek [8]. They also ob- tained a Hausdorff topology for this kind of fuzzy metric space which has very important applications in quantum particle physics, particularly in connection with both string and ∞ theory (see, [12] and references mentioned therein). Many authors have proved fixed point and common fixed point theorems in fuzzy metric spaces ( [10], [13], [16]). Regan and Abbas [14] obtained some necessary and sufficient conditions for the existence of common fixed point in fuzzy metric spaces. Recently, Cho et al [3] established some fixed point theo- rems for mappings satisfying generalized contractive condition in fuzzy metric space. The aim of this paper is to obtain common fixed point of mappings sat- isfying generalized contractive type conditions without exploiting the notion of continuity in the setting of fuzzy metric spaces. Our results generalize several comparable results in existing literature (see, [3], [2] and references mentioned therein).
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Common Fixed Point Theorems for Weakly Subsequentially Continuous Mappings in Modified Intuitionistic Fuzzy Metric Spaces

Common Fixed Point Theorems for Weakly Subsequentially Continuous Mappings in Modified Intuitionistic Fuzzy Metric Spaces

Meanwhile, jungck[16] defined the concept of compatible mappings, Jungck and Roadhes [17] generalized the last concept to the weakly compatible mappings, which is weaken than the compatible ones. Mishra et al [20] generalized the concept of compatibility in the setting of fuzzy metric spaces, he obtained some common fixed point theorems for compatible mappings in such spaces. Recently Bouhadjera and Godet Tobie [4] introduced the concept of subsequential continuity and utilized it with the concept of subcompatible mappings to establish a common fixed point, later Imdad et al.[13] improved these results and replaced subcompatibility by compatibility and subsequential continuity by reciprocal continuity, more recently, Gopal and Imdad [11] combined subsequential continuous maps with compatible maps concept to obtain some results in fuzzy metric spaces. In present work, we will generalize certain definitions to intuitionistic fuzzy metric spaces in order to obtain some common fixed point theorems by combining the concept of weakly subsequentially continuous mappings due to second author [3] with compatible of type (E) mappings given by Singh et al.[27, 28].
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Coupled Fixed Point Theorem for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces

Coupled Fixed Point Theorem for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces

The aim of present paper is to introduce the notion of t- conorm of H-type analogous to t-norm of H-type introduced by Hadzic [9] and using this notion we prove coupled fixed point theorems for weakly compatible mappings in intuitionistic fuzzy metric spaces.

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COMMON FIXED POINT THEOREM OF WEAKLY COMPATIBLE MAPPINGS OF CHAINABLE INTUITIONISTIC FUZZY METRIC SPACES

COMMON FIXED POINT THEOREM OF WEAKLY COMPATIBLE MAPPINGS OF CHAINABLE INTUITIONISTIC FUZZY METRIC SPACES

The notion of fuzzy sets was introduced by Zadeh in 1965 which laid the foundations of fuzzy set theory and fuzzy mathematics. In 1986, Atanassov generalized the notion of fuzzy sets by treating membership as a fuzzy logical value rather than a single truth value and introduced the notion of intuitionistic fuzzy sets. The intuitionistic fuzzy fixed point theory has become an area of interest for specialists in fixed point theory as intuitionistic fuzzy mathematics has covered new possibilities for fixed point theorists. In this paper, we use the idea of chainable intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four weakly compatible mappings of chainable intuitionistic fuzzy metric spaces.
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COMMON FIXED POINT THEOREMS FOR WEAKLY SUBSEQUENTIALLY CONTINUOUS MAPPINGS IN FUZZY METRIC SPACES VIA IMPLICIT RELATION

COMMON FIXED POINT THEOREMS FOR WEAKLY SUBSEQUENTIALLY CONTINUOUS MAPPINGS IN FUZZY METRIC SPACES VIA IMPLICIT RELATION

Abstract. The aim of this paper is to prove some common fixed point theorems for two weakly subsequentially continuous and compatible of type (E) pairs of self mappings satisfying an implicit relation in fuzzy metric spaces. Two examples are given to illustrate our results.

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Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Spaces

Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Spaces

In the last years, fixed point theorems have been applied to show the existence and uniqueness of the solutions of differential equations, integral equations and many other branches mathematics see, e.g., 1–3. Some common fixed point theorems for weakly commuting, compatible, δ-compatible and weakly compatible mappings under different contractive conditions in metric spaces have appeared in 4–15. Throughout this paper, X, d is a metric space.

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Common fixed theorems for weakly compatible mappings  via an implicit relation using the common (E.A) property in intuitionistic fuzzy metric spaces

Common fixed theorems for weakly compatible mappings via an implicit relation using the common (E.A) property in intuitionistic fuzzy metric spaces

The concept of Fuzzy sets was initially investigated by Zadeh [14]. Subsequently, it was developed by many authors and used in various fields. To use this concept, several researchers have defined Fuzzy metric space in various ways. In 1986, Jungck [6] introduced the notion of compatible maps for a pair of self mappings. However, the study of common fixed points of non-compatible maps is also very interesting. Aamri and El Moutawakil [15] generalized the concept of non-compatibility by defining the notion of property (E.A) and in 2005, Liu, Wu and Li [23] defined common (E.A) property in metric spaces and proved common fixed point theorems under strict contractive conditions. Jungck and Rhoades [7] initiated the study of weakly compatible maps in metric space and showed that every pair of compatible maps is weakly compatible but reverse is not true. Many results have been proved for contraction maps satisfying property (E.A) in different settings such as probabilistic metric spaces [11, 21], fuzzy metric spaces [5, 18, and 19]. Atanassov [12] introduced and studied the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets [14] and later there has been much progress in the study of intuitionistic fuzzy sets [4, 9].
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Common coupled fixed point theorems for weakly compatible mappings in fuzzy metric spaces

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,

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Common Fixed Point Theorems for Weakly Compatible Mappings by (CLR) Property on Partial Metric Space

Common Fixed Point Theorems for Weakly Compatible Mappings by (CLR) Property on Partial Metric Space

This paper mainly aims to employ the common CLR property to obtain common fixed point results for two pair of weakly compatible mappings satis- fying contractive condition of integral type on the partial metric space. Definition 1.1. [16], [20, Definition 1.1] A partial metric space (briefly P M S) is a pair (X, p) where p : X × X → R + is continuous map and R + = [0, ∞) such that for all x, y, z ∈ X :

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Common fixed point theorems via weakly compatible mappings in complete G-metric spaces: using control functions

Common fixed point theorems via weakly compatible mappings in complete G-metric spaces: using control functions

Case III. If max = 4γG(Ay, y, y), G(Ay, y, y) ≤ φ (4γ G(Ay, y, y)), G(Ay, y, y) < 4γ G(Ay, y, y), G(Ay, y, y) < G(Ay, y, y) as 3α + 7β + 6γ < 1. This leads to contradiction. Thus G(Ay, y, y) = 0 ⇒ Ay = y. Hence Ay = y and Ry = Ay ⇒ Ay = Ry = y. Hencey is common fixed point of R and A. Since y = Ay ∈ A(X ) ⊆ T (X), there exists v ∈ X such that T v = y. We prove that Bv = y.

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Common Fixed Point Theorems for Weakly Compatible Mappings Using Common Property (E.A) in Modified Intuitionistic Fuzzy Metric Space

Common Fixed Point Theorems for Weakly Compatible Mappings Using Common Property (E.A) in Modified Intuitionistic Fuzzy Metric Space

and for each W, ≥ \ here D F is standard negator. The sequence . is said to be convergent to ∈ I in the modified intuitionistic fuzzy metric space ;I, J M,N , 4= and denoted by . → J M,N if J M,N . , , K → 1 ∗ whenever → ∞ for every K > 0 . A modified intuitionistic fuzzy metric space is said to be complete if and only if every Cauchy sequence is convergent.

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Contractive Mappings and Common fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

Contractive Mappings and Common fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

Definition 2.4. [7] Let Ψ be the class of all mappings ψ : [0, 1] → [0, 1] such that ψ is continuous, non-increasing and ψ(t) < t, ∀ t ∈ (0, 1). Let Φ be the class of all mappings φ : [0, 1] → [0, 1] such that φ is continuous, non-decreasing and φ(t) > t, ∀ t ∈ (0, 1). Let (X, µ, ν, ∗, ) be an intuitionistic fuzzy metric space and ψ ∈ Ψ and φ ∈ Φ. A mapping f : X → X is called an intuitionistic fuzzy ψ-φ-contractive mapping if the following implications hold:

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

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. MSC: 54E70; 47H25

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3. COMMON FIXED POINT THEOREMS FOR SIX WEAKLY COMPATIBLE SELF-MAPPINGS IN M- FUZZY METRIC SPACES

3. COMMON FIXED POINT THEOREMS FOR SIX WEAKLY COMPATIBLE SELF-MAPPINGS IN M- FUZZY METRIC SPACES

Erceg [6], George and Veeramani [8] have introduced fuzzy metric which was used in topology and analysis. Recently Gregori et. al [10, 12] and Rafi et. al [28] have studied some property in fuzzy metric spaces. Many authors [1, 6-8, 9, 11, 13, 14, 17, 18, 25, 26, 27-33, 37, 38] have studied fixed point theory in fuzzy metric spaces.

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Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces

Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces

Bhaskar and Lakshmikantham 4, Lakshmikantham and ´ Ciri´c 5 discussed the mixed monotone mappings and gave some coupled fixed point theorems which can be used to discuss the existence and uniqueness of solution for a periodic boundary value problem. Sedghi et al. 6 gave a coupled fixed point theorem for contractions in fuzzy metric spaces, and Fang 7 gave some common fixed point theorems under φ-contractions for compatible and weakly compatible mappings in Menger probabilistic metric spaces. Many authors 8– 23 have proved fixed point theorems in intuitionistic fuzzy metric spaces or probabilistic metric spaces.
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