common coupled fixed point

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COMMON COUPLED FIXED POINT THEOREM UNDER WEAK  ψ − ϕ  CONTRACTION FOR HYBRID PAIR OF MAPPINGS WITH APPLICATION

COMMON COUPLED FIXED POINT THEOREM UNDER WEAK ψ − ϕ CONTRACTION FOR HYBRID PAIR OF MAPPINGS WITH APPLICATION

Abstract. We establish a common coupled fixed point theorem for hybrid pair of map- pings under weak ψ − ϕ contraction on a non-complete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not em- ploy the condition of continuity of any mapping involved therein. Moreover, an example and an application to integral equations are given here to illustrate the usability of the obtained results. We improve, extend, and generalize several known results.

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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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USING IMPLICIT RELATION TO PROVE COMMON COUPLED FIXED POINT THEOREMS FOR TWO HYBRID PAIRS OF MAPPINGS

USING IMPLICIT RELATION TO PROVE COMMON COUPLED FIXED POINT THEOREMS FOR TWO HYBRID PAIRS OF MAPPINGS

In this paper, we establish two common coupled fixed point theorems for two hybrid pairs of mappings satisfying an implicit relation under the conditions of weakly commuta- tivity and w−compatibility on a complete metric space, which is not partially ordered. To prove our theorems we do not use condition of continuity of any mapping. We improve, extend and generalize the result of Sedghi et al. [29].

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5. Common coupled fixed point results in partially ordered g-metric spaces

5. Common coupled fixed point results in partially ordered g-metric spaces

The notion of a coupled fixed point was introduced and studied by Guo and Lakshmikantham [18] and Bhaskar and Lakshmikantham [14]. In subsequent papers several authors proved various coupled and common coupled fixed point theorems in (partially ordered) metric spaces (see, e.g., [19, 24, 25, 37]). These results were applied for investigation of solutions of differential and integral equations. Fixed point and coupled fixed point results in partially ordered G-metric spaces were obtained in, e.g., [8, 9, 15, 16, 26, 34, 38, 39, 40].
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Applications and common coupled fixed point results in ordered partial metric spaces

Applications and common coupled fixed point results in ordered partial metric spaces

In this paper, we obtain a unique common coupled fixed point theorem by using ( ψ , α , β )-contraction in ordered partial metric spaces. We give an application to integral equations as well as homotopy theory. Also we furnish an example which supports our theorem.

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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 weakly compatible mappings in fuzzy metric spaces

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

Bhaskar and Lakshmikantham [], Lakshmikantham and Ćirić [] 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. Sedghiet al. [] gave a coupled fixed point theorem for contractions in fuzzy metric spaces, and Jin-xuan Fang [] gave some common fixed point theorems for compatible and weakly compatible φ-contractions mappings in Menger probabilistic metric spaces. Xin-Qi Hu [] proved a common fixed point theorem for mappings under ϕ -contractive conditions in fuzzy metric spaces. Many authors [–] proved fixed point theorems in (intuitionistic) fuzzy metric spaces or probabilistic metric spaces.
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Some new common coupled fixed point results in two generalized metric spaces

Some new common coupled fixed point results in two generalized metric spaces

In this manuscript, we generalize, improve, enrich and extend the above coupled fixed point results. It is worth mentioning that our results do not rely on the continuity of map- pings involved therein. We also state some examples to illustrate our results. This paper can be considered as a continuation of the remarkable works of Abbas et al. [, ] and Sabetghadam et al. [].

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Common Coupled Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

Common Coupled Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces

Abstract. In this paper, we prove some coupled fixed point theorems, which generalized the result of Hu [6], Hu et al.[7] from fuzzy metric spaces to intuitionistic fuzzy metric spaces for semi-compatible mappings, which is weaker form of compatible mappings. Keywords: Coupled fixed point, intuitionistic fuzzy metric space, coupled common fixed point, semi-compatible maps.

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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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Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property

Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property

In this work, we show that the mixed g-monotone property in common coupled fixed point theorems in ordered cone metric spaces can be replaced by another property due to Ðorić et al. []. This property is automatically satisfied in the case of a totally ordered space. Therefore, these results can be applied in a much wider class of problems. Our results generalize and extend many well-known comparable results in the literature. An illustrative example is presented in this work when our results can be used in proving the existence of a common coupled fixed point, while the results of Nashine et al. [] cannot.
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Coupled coincidence point and common coupled fixed point results in cone b-metric spaces

Coupled coincidence point and common coupled fixed point results in cone b-metric spaces

As a generalization of b-metric spaces and cone metric spaces, Hussain and Shah [] announced cone b-metric spaces, which was in . They built up some topological prop- erties in such spaces and upgraded some latest results about KKM mappings in the setting of a cone b-metric space. Hussain and Shah [] have done initial work that stimulated many authors to prove fixed point theorems, as well as common fixed point theorems for two or more mappings on cone b-metric spaces (see [–] and the references therein).

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Coupled fixed point results in cone metric spaces for -compatible mappings

Coupled fixed point results in cone metric spaces for -compatible mappings

Corollary 4. Let F : X × X ® X and g : X ® X be two mappings which satisfy all the conditions of Corollary 2. If F and g are w-compatible, then F and g have a unique common coupled fixed point. Moreover, the common fixed point of F and g is of the form (u, u) for some u Î X.

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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 Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two single valued maps. In this article, we extend these concepts to multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Two examples are presented to support our results.
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Generalized Mizoguchi-Takahashi contraction in consideration of common tripled fixed point theorem for hybrid pair of mappings

Generalized Mizoguchi-Takahashi contraction in consideration of common tripled fixed point theorem for hybrid pair of mappings

Bhaskar and Lakshmikantham [12] established some coupled fixed point theorems and applied these to study the existence and uniqueness of solution for periodic boundary value problems. Lakshmikantham and Ciric [24] proved coupled coincidence and common coupled fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces and extended the results of Bhaskar and Lakshmikantham [12].

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Some coupled fixed point theorems in two quasi-partial b-metric spaces with different coefficients

Some coupled fixed point theorems in two quasi-partial b-metric spaces with different coefficients

Consequently, (u, u) is a coupled coincidence point of F and g, and therefore (gu, gu) is a coupled point of coincidence of F and g, and by its uniqueness, we get gu = gx. Thus, we obtain F(u, u) = gu = u. Therefore, (u, u) is the unique common coupled fixed point of F and g. This completes the proof.

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Coupled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Quasi-Metric Spaces with a Q-Function

Coupled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Quasi-Metric Spaces with a Q-Function

Using the concept of a mixed g-monotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasi-metric spaces with a Q-function q. The presented theorems are generalizations of the recent coupled fixed point theorems due to Bhaskar and Lakshmikantham 2006, Lakshmikantham and ´ Ciri´c 2009 and many others.

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Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type

Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type

Theorem 3.3 . In addition to the hypotheses of Theorem 3.1., suppose that, for any (x, y), (x*, y*) Î X × X, there exists (u, v) Î X × X such that (F(u, v), F(v, u)) is comparable with (F(x, y), F(y, x)) and (F(x*, y*), F(y*, x*)). Then F and g have a unique coupled common fixed point, that is, there exists a unique (x, y) Î X × X such that x = gx = F (x, y) and y = gy = F(y, x).

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Common Tripled Fixed Point Results for Hybrid Pair of Mappings under New Condition

Common Tripled Fixed Point Results for Hybrid Pair of Mappings under New Condition

Samet and Vetro [26] introduced the concept of coupled …xed point for mul- tivalued mapping and later several authors proved existence of coupled …xed points for multivalued mappings under di¤erent conditions. Subsequently, many results in this direction were given (see, e.g., [14; 15; 16; 18; 21; 26])

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Coupled Fixed Point for (α, Ψ) Contractive in Partially Ordered Metric Spaces Using Compatible Mappings

Coupled Fixed Point for (α, Ψ) Contractive in Partially Ordered Metric Spaces Using Compatible Mappings

Later on, Lakshmikantham and Ciríc [8] proved coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces..[r]

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