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

#### 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.

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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