Multivalued Hardy-Rogers type $\mathfrak{Z}_{\Theta}$-contraction and generalized simulation functions

Abstract

The purpose of this paper is to introduce the notion of multivalued Hardy-Rogers $\mathfrak{Z}_{\Theta}$-contraction in the sense of generalized simulation functions and to present the corresponding fixed point results with some examples. Moreover, we study the strict fixed point and well-posedness, data dependence, as well as, the Ulam-Hyres stability of the fixed point problem.