Recent developments about multivalued weakly Picard operators. (English) Zbl 1326.54046

Minak, Gülhan; Altun, Ishak; Romaguera, Salvador

Bull. Belg. Math. Soc. - Simon Stevin 22, No. 3, 411-422 (2015).

Summary: In the present paper, considering a recent technique, which is used by D. Wardowski [Fixed Point Theory Appl. 2012, Article ID 94, 6 p. (2012; Zbl 1310.54074)] for fixed points of single-valued mappings, we give a new and general class of multivalued weakly Picard operators on complete metric spaces and show that the class of multivalued almost contractions (both linear and nonlinear cases in the sense of M. Berinde and V. Berinde [J. Math. Anal. Appl. 326, No. 2, 772–782 (2007; Zbl 1117.47039)]) is a proper subset of this new class. We also give a nontrivial example showing this fact.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
47H10	Fixed-point theorems

Keywords:

multivalued weakly Picard operator; multivalued almost \(F\)-contraction; fixed point

Citations:

Zbl 1310.54074; Zbl 1117.47039