Top PDF Coupled Coincidence and Common Fixed Point Theorems for Set-valued and Single-valued Mappings in fuzzy Metric Space

Coupled Coincidence and Common Fixed Point Theorems for Set-valued and Single-valued Mappings in fuzzy Metric Space

Coupled Coincidence and Common Fixed Point Theorems for Set-valued and Single-valued Mappings in fuzzy Metric Space

In this paper, we define the tangential property and the generalized coincidence property for a pair of set-valued and single-valued mappings and use it to prove some coupled co- incidence and common fixed point theorems for a hybrid pair of mappings without appeal to the completeness of the underlying space.

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Random fixed point theorems for multi valued contraction mappings in complete metric space

Random fixed point theorems for multi valued contraction mappings in complete metric space

valued map first occurs in the inverse f -1 of a single valued map f from one set S to another set P, Kuratowski valued maps also called set- valued maps or point to set map (multifunction). Other eminent mathematicians Hausdorff, Painleve and Bouligand have also valued maps. It is popular among mathematicians working in the areas of game theory & extended Banach fixed Dolhare, 2016) to multi- valued map which plays an important and vital role in the theory of variational inequalities, control theory, fractal geometry & differential inclusions. Since then the theory of valued maps become an important part to mathematicians who are working in nonlinear analysis, Volterra integral equations, nonlinear fractional differentials equations and nonlinear integral differential equations. Lot of valued functions the Brouwer’s t theorem had been extended by Kakutani in 1941 . In 1946 Eilenberg and Montgomery generalized kakutani’s result to acyclic absolute neighborhood retracts and upper semi continuous mappings.
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Coupled coincidence and coupled common fixed point theorems on a metric space with a graph

Coupled coincidence and coupled common fixed point theorems on a metric space with a graph

Very recently, some wonderful research on fixed point theory in a metric space endowed with a graph has been carried out by Alfuraidan [, ] and Alfuraidan and Khamsi []. Again, the study of coupled and common fixed point theorems remain a well motivated area of research in fixed point theory due to their applications in a wide variety of prob- lems. For example, applications of coupled fixed points for binary mappings were studied by Bhaskar and Lakshmikantham []. They have used such fixed point results to prove the existence and uniqueness of solution for a periodic boundary value problem. Recently, Chifu and Petrusel [] have developed some coupled fixed point results in metric space en- dowed with a directed graph to prove the existence of a continuous solution for a system of Fredholm and Volterra integral equations.
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Common Fixed Point Theorems in TVS-Valued Cone Metric Spaces

Common Fixed Point Theorems in TVS-Valued Cone Metric Spaces

uang and Zhang [8] generalized the notion of metric space by replacing the set of real numbers by ordered Banach space and defined cone metric space and extended Banach type fixed point theorems for contractive type mappings. Subsequently, some other authors [1,4,5,7,10,12,13,14,15,17] studied properties of cone metric spaces and fixed points results of mappings satisfying contractive type condition in cone metric spaces. Recently Beg, Azam and Arshad [6], introduced and studied topological vector space(TVS) valued cone metric spaces which is bigger than that of introduced by Huang and Zhang [8]. TVS valued cone metric spaces were further considered by some other authors in [3,9,11,16,18]. In this paper we obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition without the assumption of normality in TVS-valued cone metric spaces. Our results improve and generalize some significant recent results.
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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 , Zadeh [] introduced the concept of fuzzy sets. Then many authors gave the im- portant contribution to development of the theory of fuzzy sets and applications. George and Veeramani [, ] gave the concept of a fuzzy metric space and defined a Hausdorff topology on this fuzzy metric space, which have very important applications in quantum particle physics, particularly, in connection with both string and E-infinity theory.

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Coupled fixed point theorems for single-valued operators in b-metric spaces

Coupled fixed point theorems for single-valued operators in b-metric spaces

A nonempty set X endowed with a vector-valued metric d is called a generalized metric space in the sense of Perov (in short, a generalized metric space) and it will be denoted by (X, d). The usual notions of analysis (such as convergent sequence, Cauchy sequence, completeness, open subset, closed set, open and closed ball, etc.) are defined similarly to the case of metric spaces.

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Some Common Fixed Point Theorems For Occasionally Weakly Compatible Mappings In Complex Valued Metric Space

Some Common Fixed Point Theorems For Occasionally Weakly Compatible Mappings In Complex Valued Metric Space

The study of fixed point theorems, involving four single-valued maps, began with the assumption that all of the maps are commuted. Sessa [6] weakened the condition of commutativity to that of pairwise weakly commuting. Jungck generalized the notion of weak commutativity to that of pairwise compatible [3] and then pairwise weakly compatible maps [4]. Jungck and Rhoades [5] proved some common fixed point theorems on the concept of occasionally weakly compatible maps.

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

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

in respective fuzzy metric spaces and proved fuzzy contraction fixed point theorems under different hypotheses. For instance, Mihet assumed that the space under consideration is an M-complete non-Archimedean KM-space. Moreover, he posed an open question whether this fixed point theorem holds if the non-Archimedean fuzzy metric space is replaced by a fuzzy metric space. Vetro [] introduced a notion of weak non-Archimedean fuzzy metric space and proved common fixed point results for a pair of generalized contractive-type mappings. Wang [] gave a positive answer for the open question.
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Coupled coincidence and common fixed point theorems for hybrid pair of mappings

Coupled coincidence and common fixed point theorems for hybrid pair of mappings

Bhaskar and Lakshmikantham [3] introduced the concept of coupled fixed point of a mapping F from X ×X to X and established some coupled fixed point theorems in par- tially ordered sets. As an application, they studied the existence and uniqueness of solution for a periodic boundary value problem associated with a first order ordinary differential equation. Ć iri ć et al. [4] proved coupled common fixed point theorems for mappings satisfying nonlinear contractive conditions in partially ordered complete metric spaces and generalized the results given in [3]. Sabetghadam et al. [5] employed these concepts to obtain coupled fixed point in the frame work of cone metric spaces. Lakshmikantham and Ćirić [4] introduced the concepts of coupled coincidence and coupled common fixed point for mappings satisfying nonlinear contractive conditions in partially ordered complete metric spaces. The study of fixed points for multi-valued contractions mappings using the Hausdorff metric was initiated by Nadler [1] and Markin [6]. Later, an interesting and rich fixed point theory for such maps was devel- oped which has found applications in control theory, convex optimization, differential inclusion and economics (see [7] and references therein). Klim and Wardowski [8] also obtained existence of fixed point for set-valued contractions in complete metric spaces. Dhage [9,10] established hybrid fixed point theorems and gave some applications (see also [11]). Hong in his recent study [12] proved hybrid fixed point theorems involving multi-valued operators which satisfy weakly generalized contractive conditions in ordered complete metric spaces. The study of coincidence point and common fixed points of hybrid pair of mappings in Banach spaces and metric spaces is interesting and well developed. For applications of hybrid fixed point theory we refer to [13-16]. For a survey of fixed point theory and coincidences of multimaps, their applications and related results, we refer to [16-22].
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Common Fixed Point Theorems for Pair of Generalized Multi-valued Mappings in Cone Metric Spaces

Common Fixed Point Theorems for Pair of Generalized Multi-valued Mappings in Cone Metric Spaces

In 1970, Covitz Nadler’s (see [6]) gave the following results “Multi-valued contraction mappings generalized metric spaces” using this result. H. E. Kunze et, al (see [3]) introduce an iterative method involving projections that guarantees convergence, from any starting point to a point the set of all fixed points of a multifunction operator T. The results [3] were generalized by Dubey [16]. Especially, Nadler’s. Jr. [7] gave a generalization of Banach’s contraction principle to the case of set-valued maps in metric spaces. Recently, Huang and Zhang [1] introduced the concept of cone metric space by replacing the set of real numbers by an ordered Banach space and obtain some fixed point theorems for mappings satisfying different contractive conditions. Subsequently, the results [1] were generalized and studied the existence of common fixed points of a pair of self mappings satisfying a contractive type condition in the frame work of normal cone metric spaces, see for instance [2], [4], [5],[9] and [11]. The authors [10, 14] introduced the concept of multi-valued contractions in cone metric spaces and using the notion of normal cones, obtained fixed point theorems for such mappings. As we know, most of known cones are normal with normal constant . Further, the author [12] and [13] proved two results, fixed points and common fixed points of multifunction on cone metric spaces. These results also generalized by Dubey and Narayan [17].In this paper, we prove common fixed point theorems for pair of multi-valued maps in cone metric spaces with normal constant K=1, which generalize and extend the results of [1], [8] and [15].
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Some common coupled fixed point theorems for generalized contraction mappings in C∗ algebras-valued b-metric spaces

Some common coupled fixed point theorems for generalized contraction mappings in C∗ algebras-valued b-metric spaces

The notion of b-metric space was introduced by Bakhtin in[1]. Since then, many actions generalized the b-metric spaces(see [2], [3], [4]). Recently, Ma and Jiang[5] introduced the concept of a C ∗ algebras-valued b-metric spaces,and they obtained the basic fixed point theo- rems for self-map with contractive condition in C ∗ algebras-valued b-metric spaces. In 2016, Kamranetal [6] also introduced the concept of this space, and generalized the Banach contrac- tion principle on this space.

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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

Then there exist x ∈ X such that x Fx, x, that is, F admits a unique fixed point in X. Let φt kt, where 0 < k < 1, the following by Lemma 1, we get the following. Corollary 2 see 6. Let a ∗ b ≥ ab for all a, b ∈ 0, 1 and X, M, ∗ be a complete fuzzy metric space such that M has n-property. Let F : X × X → X and g : X → X be two functions such that

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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

Since Zadeh [1] introduced the concept of fuzzy sets, many authors have extensively developed the theory of fuzzy sets and applications. George and Veeramani [2, 3] gave the concept of fuzzy metric space and defined a Hausdorff topology on this fuzzy metric space which have very important applications in quantum particle physics particularly in connection with both string and infinity theory.

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Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces

Coupled coincidence point and common coupled fixed point theorems in complex valued metric spaces

Theorem 2.9. Let (X, d) be a complex valued metric space, F : X × X → X and g : X → X be two mappings which satisfy all the conditions of Theorem 2.5. If F and g are w−compatible, then F and g have unique common coupled fixed point. Moreover, common fixed point of F and g has the form (u, u) for some u ∈ X.

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A common coupled fixed point result in complex valued metric space for two mappings

A common coupled fixed point result in complex valued metric space for two mappings

One of the main pillar in the study of fixed point theory is Banach Contraction priciple which was done by Banach in 1922. Fixed In 2011 Akbar Azam et al., 2011 introduced the concept of complex valued metric space. The concept of coupled fixed point was first introduced by Bhaskar and Laxikantham in 2006. Recently some researchers prove some coupled fixed point theorems in complex valued metric space in (Kang et al., 2013;

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Fixed point and coincidence point theorems for a pair of single valued and multi valued maps on a metric space

Fixed point and coincidence point theorems for a pair of single valued and multi valued maps on a metric space

Throughout, unless otherwise stated, (X,d) is a metric space, K(X) is the collec- tion of all nonempty compact subsets of X , CL (X) is the collection of all nonempty closed subsets of X , H is the extended Hausdorff metric on CL (X) , F is a map- ping from X into CL (X) , f , S are self-maps on X , I is the identity map on X , for any self-map h on X , (h) = {hx : x ∈ X}, R + is the set of all nonnegative real numbers, N is the set of all positive integers, Ω : (R + ) 5 → R + is monotonically in-

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Fixed point theorems of multi-valued and single-valued mappings in partial metric spaces

Fixed point theorems of multi-valued and single-valued mappings in partial metric spaces

Theorem 1.1 [1] Let (X , d) be a complete metric space, and F : X → CB(X) is a multivalued mapping, where CB(X) is the set of all nonempty closed bounded subsets of X . Assume that there exists α ∈ [0, 1) such that H(Fx, Fy) ≤ α d(x, y) for all x, y ∈ X . Then F has a fixed point. The Nadler’s fixed point theorem has been generalized in many ways. One generalization of Nadler’s fixed point theorem was given by Reich in 1972 [3], which was followed with a relaxed condition by Mizoguchi and Takahashi in 1989 [4] where they used the concept of M T −function ( R −function).
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Fixed point sets of set-valued mappings

Fixed point sets of set-valued mappings

directly from () and the fact that F(x) is closed for each x ∈ X. We now recall some definitions of continuity for set-valued mappings (see [] for more details). For our purpose, let X and Y be metric spaces (with no ambiguity, their metrics will be denoted by the same symbol ‘d’). A set-valued mapping F : X →  Y is said to be

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Coupled fixed point theorems in complex valued G_b-metric spaces

Coupled fixed point theorems in complex valued G_b-metric spaces

E. Ozgur [15] presented the notion of complex valued G b -metric space. In 2006, Bhaskar et al. [5] introduced the notion of coupled fixed point and proved some fixed point results in this context. Similarly, we introduced the notion of coupled fixed point for a mapping in complex valued G b -metric spaces.

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Some fixed point theorems for set valued directional contraction mappings

Some fixed point theorems for set valued directional contraction mappings

In this paper, we prove a fixed point theorem for set valued directional contraction mappings.. see definition below..[r]

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