Common Coupled Fixed Point Theorems of Mixed Monotone Mapping Pairs in Partially Ordered Metric Spaces

2009 ◽  
Author(s):  
Xinqi Hu ◽  
Fenxiu Zhu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Monotone Mapping ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Common Coupled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Mixed Monotone Mapping

scholarly journals Common Coupled Fixed Point Theorem for Geraghty-Type Contraction in Partially Ordered Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiao-lan Liu ◽  
Mi Zhou ◽  
Boško Damjanović
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Common Coupled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Weakly Compatible ◽  
Common Limit Range Property ◽  
Type Contraction

We study the existence and uniqueness of common coupled fixed point of four self-mappings for Geraghty-type contraction using weakly compatible mappings in partially ordered metric spaces with common limit range property (denoted by (CLRST)), the property of E.A, and so on. It is noted that the continuity of mappings and completeness of spaces can be removed. Our results improve, extend, complement, and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.

scholarly journals Tripled Fixed Points of Multivalued Nonlinear Contraction Mappings in Partially Ordered Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Mujahid Abbas ◽  
Hassen Aydi ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Contraction

Berinde and Borcut (2011), introduced the concept of tripled fixed point for single mappings in partially ordered metric spaces. Samet and Vetro (2011) established some coupled fixed point theorems for multivalued nonlinear contraction mappings in partially ordered metric spaces. In this paper, we obtain existence of tripled fixed point of multivalued nonlinear contraction mappings in the framework of partially ordered metric spaces. Also, we give an example.

scholarly journals New Fixed Point Theorems and Application of Mixed Monotone Mappings in Partially Ordered Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Li Liu ◽  
Anmin Mao ◽  
Yingying Shi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Monotone Mapping ◽  
Coupled Fixed Point ◽  
Monotone Mappings ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Uniqueness Results

We consider the existence of a coupled fixed point for mixed monotone mapping F:X×X→X satisfying a new contractive inequality which involves an altering distance function in partially ordered metric spaces. We also establish some uniqueness results for coupled fixed points, as well as the existence of fixed points of mixed monotone operators. The presented results generalize and develop some existing results. In addition to an example as well as an application, we establish some uniqueness results for a system of integral equations.

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