Common Fixed Points of Multi-valued Mappings with Application to Integral Equations

Recently, B. Samet, C. Vetro and P. Vetro introduced the notion of $\alpha-\psi-$contractive type mappings and established some fixed point theorems for the mappings in complete metric spaces. In this paper, with the motivation of $\alpha-\psi-$contractiveness of a mapping $T$ on a metric space, we introduce a new notion of coupled $\alpha_*-g-$contractiveness of two mappings $ T $ and $ S $ on a metric space. Then, considering this notion, some common fixed point results have been obtained. Moreover, some examples and applications to integral equations are given to illustrate the usability of the obtained results.