Coupled fixed point theorems for ϕ\phiϕ-contractive mixed monotone mappings in partially ordered metric spaces (original) (raw)
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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.
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.
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.
2013
In some recent papers, a method was developed of reducing coupled fixed point problems in (ordered) metric and various generalized metric spaces to the respective results for mappings with one variable. In this paper, we apply the mentioned method and obtain some coupled fixed point results for mappings satisfying ϕ-weak contractive conditions in ordered b-metric spaces. Examples show how these results can be used. Finally, an application to nonlinear Fredholm integral equations is presented, illustrating 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].
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. TMA 65 (2006) 1379-1393] by significantly weakening the involved contractive condition. Our technique of proof is essentially different and more natural. An example as well an application to periodic BVP are also given in order to illustrate the effectiveness of our generalizations.
Coupled fixed point theorems for nonlinear contractions without mixed monotone property
Fixed Point Theory and Applications, 2012
In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fixed point of the given mapping. Further, we apply our results to the existence of a coupled fixed point of the given mapping in partially ordered metric spaces. Moreover, some applications to integral equations are presented. MSC: 47H10; 54H25