scholarly journals Coupled Fixed Points Results for Nonlinear Contractions in Quasi-ordered Metric Spaces

2015 ◽  
Vol 8 (1) ◽  
pp. 1-7
Author(s):  
Vishal Gupta
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Nonlinear Contractions ◽  
Coupled Fixed Points

scholarly journals Tripled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Erdal Karapınar ◽  
Amaresh Kundu
Keyword(s):  
Fixed Points ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Triple Coincidence ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Contractions ◽  
Coupled Fixed Points

Tripled fixed points are extensions of the idea of coupled fixed points introduced in a recent paper by Berinde and Borcut, 2011. Here using a separate methodology we extend this result to a triple coincidence point theorem in partially ordered metric spaces. We have defined several concepts pertaining to our results. The main results have several corollaries and an illustrative example. The example shows that the extension proved here is actual and also the main theorem properly contains all its corollaries.

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

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