Multivalued [formula omitted]-weakly Picard mappings

Abstract

Recently, M. Berinde and V. Berinde [M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. (in press)] extended the notion of weak contraction from single valued mappings to multivalued mappings and obtained some convergence theorems for the Picard iteration associated with multivalued weak contractions. We further extended the notion of weak contraction and introduced the notions of multivalued f -weak contraction and generalized multivalued f -weak contraction. We obtain some coincidence and fixed point theorems. Our results extend [M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. (in press)] and those contained therein.