New fixed point theorems for asymptotically regular multi-valued maps

Recently, extending Ćirić’s quasi-contraction to a very general setting, Proinov [Petko D. Proinov, Fixed point theorems in metric spaces, Nonlinear Anal. 64 (2006) 546–557] obtained a remarkable fixed point theorem. We utilize Proinov’s contractive type hypotheses for a self-map of a metric space to obtain very general fixed point theorems for multi-valued maps in metric spaces.