Coupled Fixed Point Theorems for ()-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications
Coupled Fixed Point Theorems for ()-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications
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DOI：
10.1155/2014/586096
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发表时间：
2014-03
期刊：
影响因子：
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通讯作者：
M. Jain;N. Gupta;Sanjay Kumar
中科院分区：
文献类型：
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作者：
M. Jain;N. Gupta;Sanjay Kumar
本文的目的是建立部分有序度量空间中混合单调算子在(,)-收缩条件下的耦合不动点的存在唯一性。所提出的工作概括了Berinde（2011年，2012年）的最新结果，并削弱了Bhaskar和Lakshmikantham（2006年）以及Luong和Thuan（2011年）的著名结果中涉及的收缩条件。通过一个合适的算例验证了本文工作的有效性。作为应用，给出了一类非线性积分方程解的存在唯一性结果。
The object of this paper is to establish the existence and uniqueness of coupled fixed points under a ( , )-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.