Fixed points of monotone mappings and application to integral equations (original) (raw)
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Coupled fixed point theorems for mixed monotone mappings and an application to integral equations
Computers & Mathematics with Applications, 2011
In this paper, we extend the coupled fixed point theorems for a mixed monotone mapping F : X × X → X in partially ordered metric spaces established by Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. An application to nonlinear integral equations is also given to illustrate our results.
Nonlinear Analysis-theory Methods & Applications, 2012
In this paper we extend the coupled fixed point theorems for mixed monotone operators F : X × X → X obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.
2011
In this paper we extend the coupled fixed point theorems for mixed monotone operators F:X × X → X obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.
2016
In this paper we extend the coupled fixed point theorems for mixed monotone operators F : X × X → X obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.
Differential Equations & Applications
In this paper, the author presents some generalizations of a measure theoretic hybrid fixed point theorem of Dhage for the monotone nondecreasing mappings in a partially ordered metric space and then applies to a nonlinear functional integral equation for proving the existence as well as local ultimate attractivity of the comparable solutions defined on a unbounded interval of real line. An algorithm is constructed and it is shown that the sequence of successive approximations of the considered integral equation converges monotonically to the solution under weak partial Lipschitz and partial compactness type conditions.
arXiv (Cornell University), 2011
In this paper we extend the coupled fixed point theorems for mixed monotone operators F : X × X → X obtained in [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983-992], by weakening the involved contractive condition. An example as well an application to nonlinear Fredholm integral equations are also given in order to illustrate the effectiveness of our generalizations.
Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces
Mathematical and Computer Modelling, 2012
a b s t r a c t We establish coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving two altering distance functions in ordered partial metric spaces. Presented theorems extend and generalize the results of Bhaskar and Lakshmikantham [T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393] and Harjani et al. [J. Harjani, B. López and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011) 1749-1760].