Coupled fixed point theorems with respect to binary relations in metric spaces

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Authors
Mohammad Sadegh Asgari
 Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Baharak Mousavi
 Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Abstract
In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with
a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in
this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed
to hold on elements that are comparable in the binary relation. Next on the basis of the coupled fixed
point theorems, we prove the existence and uniqueness of positive definite solutions of a nonlinear matrix
equation.
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ISRP Style
Mohammad Sadegh Asgari, Baharak Mousavi, Coupled fixed point theorems with respect to binary relations in metric spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 2, 153162
AMA Style
Asgari Mohammad Sadegh, Mousavi Baharak, Coupled fixed point theorems with respect to binary relations in metric spaces. J. Nonlinear Sci. Appl. (2015); 8(2):153162
Chicago/Turabian Style
Asgari, Mohammad Sadegh, Mousavi, Baharak. "Coupled fixed point theorems with respect to binary relations in metric spaces." Journal of Nonlinear Sciences and Applications, 8, no. 2 (2015): 153162
Keywords
 Coupled fixed point
 reflexive relation
 matrix equations
 positive define solution.
MSC
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