Nonlinear coupled coincidence and coupled fixed point theorems for not necessary commutative contractive mappings in partially ordered probabilistic metric spaces

作者：Doric Dragan^*

来源：Applied Mathematics and Computation, 2013, 219(11): 5926-5935.

DOI：10.1016/j.amc.2012.12.047

• Probabilistic metric space
• Coupled coincidence point
• Coupled fixed point
• Partially ordered set
• Mixed monotone mapping

In this paper we introduce the notion of compatibility of mappings in partially ordered probabilistic metric spaces and use this notion to establish a coupled coincidence point result. Very recently Hu and Ma [Xin-qi Hu, Xiao-yan Ma, Coupled coincidence point theorems under contractive conditions in partially ordered probabilistic metric spaces, Nonlinear Anal. 74 (2011) 6451-6458] proved coupled coincidence point theorems for commuting mappings in partially ordered probabilistic metric spaces. In this paper we proved results of Hu and Ma under a different set of conditions. Precisely, we establish our results by assuming that two mappings on a partially ordered probabilistic metric spaces are compatible (not necessary commutative) and satisfy a more general contractive condition than the contractive condition in the main theorem of Hu and Ma. Our results improve and extend a coupled coincidence point theorem due to Hu and Ma, as well as a coupled fixed point theorem due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393]. An example is given to support our result.

• 出版日期2013-2-1