Some Common Fixed Point Results in Partially Ordered Metric Spaces for Generalized Rational Type Contraction Mappings

2013 ◽  
Vol 41 (3) ◽  
pp. 323-331 ◽  
Author(s):  
Sumit Chandok ◽  
Tulsi Dass Narang ◽  
Mohamed-Aziz Taoudi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type ◽  
Type Contraction

scholarly journals Generalized fixed point results of rational type contractions in partially ordered metric spaces

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
N. Seshagiri Rao ◽  
K. Kalyani
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Type ◽  
Type Contraction

Abstract Objectives We investigated the existence and uniqueness of a fixed point for the mapping satisfying generalized rational type contraction conditions in metric space endowed with partial order. Suitable examples are presented to justify the results obtained. Result Some new fixed point results have been obtained for a mapping fulfilling generalized contractions. The uniqueness of the fixed point is also the part of the study based on an ordered relation. One example is given for a result which is not valid in the usual metric space.

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 Common Fixed Point of (ψ, β)-Generalized Contractive Mappings in Partially Ordered Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Abbas ◽  
I. Zulfaqar ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings

Gordji et al. (2012) gave a generalization of Geraghty’s theorem. The aim of this paper is to study the necessary conditions for the existence of coincidence and common fixed point of four mappings satisfying (ψ, β)-generalized contractive condition in the setup of partial ordered metric spaces. Some examples are given to validate the definitions and results presented herein.

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