ON A NEW CLASS OF MULTIVALUED WEAKLY PICARD OPERATORS ON COMPLETE METRIC SPACES

Abstract

In the present paper, the concept of nonlinear $F$-contraction formultivalued mappings in metric spaces is introduced and considering the new proof technique, which was used for single valued maps by Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 2012:94, 6 pp.], we demonstrate that multivalued nonlinear $F$-contractions of Ćirić type are weakly Picard operators on complete metric spaces. Finally, we give a nontrivial example to guarantee that our result is veritable generalization of recent result of Ćirić [Lj. B. Ćirić, Multi-valued nonlinear contraction mappings, Nonlinear Analysis, 71 (2009), 2716-2723]. Also, we show that many fixed point results in the literature can not be applied to this example.