Some Proximally Coincidence Points for Non-self Mappings and Self Mappings in Partially Ordered Metric Spaces

R. Wangkeeree, N. Sisarat

Abstract

In this paper, we first introduce the concept of proximally coincidence points for non-self mapping and self mappings. We prove the existence of a proximally coincidence point for non-self mappings and self mapping satisfying the $(\psi ,\alpha ,\beta)$-contractive conditions in the setting of partially ordered set which is endowed with a metric. Further, our result provides an extension of a result due to Binayak and Amaresh [Binayak and Amaresh, A best proximity point theorem for weakly contractive non-self-mappings. Nonlinear Anal. 74(14), 48044808 (2011)] to the case of non-self-mapping. The examples illustrating our results are given