Coupled Coincidence Research Articles

Coupled Coincidence Point Theorems for New Types of Mixed Monotone Multivalued Mappings in Partially Ordered Metric Spaces

We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are also given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings.

Coupled Coincidence Point Theorems for α-ψ-Contractive Type Mappings in G-Metric Spaces

Coupled Coincidence Point Theorems for α-ψ-Contractive Type Mappings in G-Metric Spaces

Coupled coincidence point theorems for \phi-contractive under (F,g)-invariant set in complete metric space

In this paper, we prove existence of a coupled coincidence point theorem and coupled common fixed point theorem for φ-contractive mappings in partially ordered complete metric space without the mixed g-monotone property by using the concept of an (F, g)-invariant set. We prove some coupled fixed point theorems for such nonlinear contractive mappings in a complete metric space.Our results are generalization of the results of Wutiphol Sintunavarat, Poom Kumam and Yeol Je Cho (Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications 2012,2012:170.).

Coupled coincidence point result in partially ordered generalized metric spaces

The present study introduces the notion of compatibility in partially ordered G-metric spaces and uses this perception to establish a coupled coincidence point result. Our effort extend the recent work of Choudhary and Maity [B. S. Choudhary, P. Maity, Coupled fixed point results in generalized metric spaces, Mathematical and Computer Modelling 54 (2011) 73-79]. The example demonstrates that our main result is an actual improvement over the results which are generalized

Coupled coincidence point result in partially ordered generalized metric spaces

The present study introduces the notion of compatibility in partially ordered G-metric spaces and uses this perception to establish a coupled coincidence point result. Our effort extend the recent work of Choudhary and Maity [B. S. Choudhary, P. Maity, Coupled fixed point results in generalized metric spaces, Mathematical and Computer Modelling 54 (2011) 73-79]. The example demonstrates that our main result is an actual improvement over the results which are generalized

Coupled coincidence point results on generalized distance in ordered cone metric spaces

In this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via c-distance. We also proved some related coupled common fixed point theorems for such mappings. Our results general- ize,extend,andunifyseveralwell-knowncomparableresultsintheliteratureregarding this topic. We present some examples to illustrate the concepts and results.

Coupled coincidence point theorems for contractions in generalized fuzzy metric spaces

In this paper, we introduce the concept of a mixed g-monotone mapping and prove coupled coincidence and common coupled fixed point theorems for mappings under ϕ-contractive conditions in partially ordered generalized fuzzy metric spaces. We also give an example to illustrate the theorems. MSC:47H10, 54H25.

Coupled Coincidence and Common Fixed Point Theorems in Menger PM Spaces

Recently Many results on coupled xed point theory exist in the literature, for more de-tails, one can see in [2,11,22]. We established coupled coincidence and common xed point theoremsfor two self mixed g-monotone mappings in the settings of Menger PM-spaces. Our result is alsosubstantiated with the aid of an appropriate example and some open problems are also suggestedfor further studies

Coupled coincidence point results for compatible mappings in partially ordered fuzzy metric spaces

Coupled fixed point problems have attracted much attention in recent times. In this paper we establish coupled coincidence point and coupled fixed point results in the context of fuzzy metric spaces. The two mappings considered here are assumed to be compatible. Hadžić type t-norm is used. By an application of the coincidence point theorem in fuzzy metric spaces, a corresponding result is obtained in metric spaces. The main theorem of this paper is illustrated with an example. Our work extends some existing results.

Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces

This paper is concerned with mixed g-monotone mappings in partially ordered metric spaces. We establish several coupled coincidence and coupled common fixed point theorems, which generalize and complement some known results. Especially, our main results complement some recent results due to Lakshmikantham and Ciric. Two examples are given to illustrate the usability of our results. Mathematics Subject Classification(2010): 47H10, 54H25.

Coupled coincidence points for two mappings in metric spaces and cone metric spaces

This article is concerned with coupled coincidence points and common fixed points for two mappings in metric spaces and cone metric spaces. We first establish a coupled coincidence point theorem for two mappings and a common fixed point theorem for two w-compatible mappings in metric spaces. Then, by using a scalarization method, we extend our main theorems to cone metric spaces. Our results generalize and complement several earlier results in the literature. Especially, our main results complement a very recent result due to Abbas et al.

Coupled coincidence points for mixed monotone operators in partially ordered metric spaces

In this paper, we give and prove some coupled coincidence point theorems for mappings F : X × X → X and g : X → X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65:1379–1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4):16–24, 2010), Harjani et al. (Nonlinear Anal 74:1749–1760, 2011) and Choudhury et al. (Ann Univ Ferrara 57:1–16, 2011). We also give some examples to illustrate our results.

Coupled coincidence points for compatible mappings satisfying mixed monotone property

Coupled coincidence points for compatible mappings satisfying mixed monotone property

Coupled coincidence point theorems for mixed monotone nonlinear operators

We obtain coupled coincidence and coupled common fixed point theorems for mixed g-monotone nonlinear operators F:X×X→X in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341–4349], of coupled fixed point theorems established by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393] and also include as particular cases several related results in very recent literature.

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 Ciric 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. 2000 Mathematics Subject Classification: 47H10; 47H04; 47H07.

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 coincidence and common fixed point theorems for a hybrid pair of mappings without appeal to the completeness of the underlying space.

Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir‐Keeler Type Contractions

We prove coupled coincidence point and coupled fixed point results of F : X × X → X and g : X → X involving Meir‐Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application.

Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with a c‐Distance

Cho et al. (2012) proved some coupled fixed point theorems in partially ordered cone metric spaces by using the concept of a c‐distance in cone metric spaces. In this paper, we prove some coincidence point theorems in partially ordered cone metric spaces by using the notion of a c‐distance. Our results generalize several well‐known comparable results in the literature. Also, we introduce an example to support the usability of our results.

Coupled Coincidence Point Theorem in Partially Ordered Metric Spaces via Implicit Relation

We prove a coupled coincidence point theorem for mappings F : X × X → X and g : X → X, where F has the mixed g‐monotone property, in partially ordered metric spaces via implicit relations. Our result extends and improves several results in the literature. Examples are also given to illustrate our work.

Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces

New coupled coincidence point and coupled fixed point results in ordered partial metric spaces under the contractive conditions of Geraghty, Rakotch, and Branciari types are obtained. Examples show that these results are distinct from the known ones.