Coupled Fixed Point Theorems $\alpha_*-\psi-$contractive On Partially Ordered Metric Space

In 1987, Guo and Lakshmikantham introduced the notion of coupled fixed points. There exist a lot of works done on the coupled fixed points of some types of mappings. Recently, the notion of $\alpha-\psi-$contractive type mappings has been introduced by Samet et al. in 2012. In this paper, we introduce $\alpha_*-\psi-$contractive multifunctions on a partially ordered metric space and provide some results about coupled fixed points without upper semi-continuity condition.