Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications

Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mappingFfromX×XintoXand a mappinggfromXintoXwith some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalizedg-Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalizedg-Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.

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Coupled Fixed Point Theorems with Rational Type Contractive Condition in a Partially OrderedG-Metric Space

Journal of Mathematics ◽

10.1155/2014/785357 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

K. Chakrabarti

Keyword(s):

Fixed Point ◽

Metric Space ◽

Fixed Point Theorems ◽

Coupled Fixed Point ◽

Contractive Condition ◽

Mixed Monotone Property ◽

Coincidence Points ◽

Coupled Coincidence Points ◽

Rational Type ◽

Coupled Coincidence

Coupled fixed point theorems for a map satisfying mixed monotone property and a nonlinear, rational type contractive condition are established in a partially orderedG-metric space. The conditions for uniqueness of the coupled fixed point are discussed. We also present results for the existence of coupled coincidence points of two maps.

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Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces

Abstract and Applied Analysis ◽

10.1155/2012/192581 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Cited By ~ 16

Author(s):

Zorana Golubović ◽

Zoran Kadelburg ◽

Stojan Radenović

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Coincidence Point ◽

Coupled Fixed Point ◽

Coupled Coincidence Point ◽

Partial Metric ◽

Coincidence Points ◽

Coupled Coincidence Points ◽

Partial Metric Spaces ◽

Coupled Coincidence

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.

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Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with ac-Distance

Journal of Applied Mathematics ◽

10.1155/2012/312078 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 6

Author(s):

Wasfi Shatanawi ◽

Erdal Karapınar ◽

Hassen Aydi

Keyword(s):

Fixed Point Theorems ◽

Metric Spaces ◽

Coincidence Point ◽

Coupled Fixed Point ◽

Coincidence Points ◽

Cone Metric Spaces ◽

Partially Ordered ◽

Coupled Coincidence Points ◽

Cone Metric ◽

Coupled Coincidence

Cho et al. (2012) proved some coupled fixed point theorems in partially ordered cone metric spaces by using the concept of ac-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 ac-distance. Our results generalize several well-known comparable results in the literature. Also, we introduce an example to support the usability of our results.

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

Abstract and Applied Analysis ◽

10.1155/2012/781563 ◽

2012 ◽

Vol 2012 ◽

pp. 1-22 ◽

Cited By ~ 2

Author(s):

Hassen Aydi ◽

Erdal Karapınar ◽

İnci M. Erhan

Keyword(s):

Fixed Point ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Coincidence Point ◽

Coupled Fixed Point ◽

Coupled Coincidence Point ◽

Ordered Metric Spaces ◽

Partially Ordered Metric Spaces ◽

Partially Ordered ◽

Coupled Coincidence

We prove coupled coincidence point and coupled fixed point results of and 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.

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