Fixed point results for multivalued mapping with closed graphs in generalized Banach spaces

TL;DR

This paper establishes new fixed point theorems for multi-valued mappings with closed graphs in generalized Banach spaces, extending classical results and applying to nonlinear inclusion systems.

Contribution

It introduces a new characterization of upper semi-continuity for multi-valued mappings and proves Perov and Krasnoselskii type fixed point theorems in this setting.

Findings

Fixed point theorems for multi-valued mappings with closed graphs.

Application to nonlinear inclusion systems.

Extension of classical fixed point results to generalized Banach spaces.

Abstract

In this paper, by establishing a new characterization of the notion of upper semi-continuity of multi-valued mappings in generalized Banach spaces, we prove some Perov type fixed point theorems for multi-valued mappings with closed graphs. Moreover, we derive some Krasnoselskii's fixe point results for multi-valued mappings in generalized Banach spaces. Our results are applied to a large class of nonlinear inclusions systems.