scholarly journals Best Proximity Points for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Weak Contraction ◽  
Ordered Metric Spaces ◽  
Best Proximity Points ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Expression ◽  
Rational Type

We introduce a generalized proximal weak contraction of rational type for the non-self-map and proved results to ensure the existence and uniqueness of best proximity point for such mappings in the setting of partially ordered metric spaces. Further, our results provides an extension of a result due to Luong and Thuan (2011) and also it provides an extension of Harjani (2010) to the case of self-mappings.

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 Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 6913-6928
Author(s):  
Raju Gopi ◽  
◽  
Veerasamy Pragadeeswarar ◽  
Choonkil Park ◽  
Dong Yun Shin ◽  
...  
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Common Best Proximity Point ◽  
Nonlinear Contractions
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