Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces

2011 ◽  
Vol 74 (17) ◽  
pp. 6451-6458 ◽  
Author(s):  
Xin-qi Hu ◽  
Xiao-yan Ma
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Probabilistic Metric Spaces ◽  
Partially Ordered ◽  
Probabilistic Metric ◽  
Coupled Coincidence

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

2014 ◽  
Vol 07 (02) ◽  
pp. 1450009 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Pradyut Das
Keyword(s):  
Partial Order ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Compatible Mappings ◽  
Probabilistic Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Probabilistic Metric ◽  
Coupled Coincidence

In this paper, we establish coupled coincidence point results in probabilistic metric spaces with a partial order. The main theorem has several corollaries and is supported with an example. The corollaries are shown to be properly contained in the main theorem. By an application of a corollary we obtained a corresponding result in metric spaces which is also supported with an example. Some results in [Nonlinear Anal. 74 (2011) 6451–6458] and [Nonlinear Anal. 71 (2009) 1833–1843] are extended in this paper. The extensions are shown to be actual with the help of an example. We use Hadžić type t-norm in this paper. The methodology of the proofs in this work is a blending of analytic and order theoretic approaches.

Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Jamshaid Ahmad ◽  
Muhammad Arshad ◽  
Pasquale Vetro
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Coupled Coincidence

Abstract.In this paper, we extend the coupled coincidence point theorems for a mixed

scholarly journals Some fixed point results of generalized $$(\phi , \psi )$$-contractive mappings in ordered b-metric spaces

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Belay Mitiku ◽  
Kalyani Karusala ◽  
Seshagiri Rao Namana
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Common Fixed Points ◽  
Coupled Coincidence Point ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Contractive Mappings ◽  
Coupled Coincidence

Abstract Objectives The aim of this paper is to establish some fixed point, coincidence point and, coupled coincidence and coupled common fixed point results for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive mappings in partially ordered b-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. Few examples are illustrated to justify our results. Result The existence and uniqueness theorems for a fixed point and coincidence point, coupled coincidence point and coupled common fixed points for two mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -contractive conditions in complete partially ordered b-metric spaces are proved. These results generalize several comparable results in the existing literature.

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

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Nguyen Manh Hung ◽  
Erdal Karapınar ◽  
Nguyen Van Luong
Keyword(s):  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Partially Ordered Metric Spaces ◽  
Monotone Property ◽  
Partially Ordered ◽  
Coupled Coincidence

We prove a coupled coincidence point theorem for mappingsF: andg: , whereFhas the mixedg-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.

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