Data dependence, strict fixed point results, and well-posedness of multivalued weakly Picard operators (Q2034573)

Summary: In this paper, we introduce the notion of \((\mathfrak{s},\mathfrak{r})\)-contractive multivalued weakly Picard operators via simulation functions, named as \(\mathcal{Z}_{(\mathfrak{s},\mathfrak{r})}\)-contractions. We present some related fixed point theorems. We investigate data dependence and strict fixed point results. The well-posedness for such operators is also considered. Moreover, we generalize the results of \textit{G. Moţ} and \textit{A. Petruşel} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, 3371--3377 (2009; Zbl 1213.54068)]. To show the usability of our results, we give some examples and an application to resolve a functional equation arising in dynamical systems.