zbMATH — the first resource for mathematics

On a new class of multivalued weakly Picard operators on complete metric spaces. (English) Zbl 1357.54029
Summary: 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 D. Wardowski [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)], 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 L. Ćirić [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7–8, 2716–2723 (2009; Zbl 1179.54053)]. Also, we show that many fixed point results in the literature can not be applied to this example.

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
Full Text: DOI