A new fixed point result and its application to existence theorem for nonconvex Hammerstein type integral inclusions

Abstract

In this paper, a generalization of Nadler's fixed point theorem is presented for $H^+$-type $k$-multi-valued weak contractive mappings. We consider a nonconvex Hammerstein type integral inclusion and prove an existence theorem by using an $H^+$-type multi-valued weak contractive mapping.

Keywords

• multi-valued contraction map
• k-multi-valued weak contractive map
• h+-type multi-valued weak contractive map
• hammerstein type integral inclusion
• fixed point