A generalization of Nadler’s fixed point theorem and its application to nonconvex integral inclusions

Hemant Kumar Pathak, Naseer Shahzad

Abstract


In this paper, a generalization of Nadler's
fixed point theorem is presented. In the sequel, we consider
a nonconvex integral inclusion and prove a Filippov type existence
theorem by using an appropriate norm on the space of selection of
the multifunction and a $H^+$-type contraction for set-valued maps.

Keywords


$H^+$-type multi-valued nonexpansive mapping; demiclosed mapping; Opial's condition; $\sigma$-algebra; Bochner integrable functions

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