A multivalued version of Krasnoselskii’s theorem in generalized Banach spaces

Abstract

The purpose of this paper is to extend Krasnoselskii’s fixed point theorem to the case of generalized Banach spaces for multivalued operators. As application, we will give an existence result for a system of Fredholm-Volterra type differential inclusions.

Keywords

• compact operator
• fixed point
• generalized contraction
• generalized banach space
• generalized metric space
• integral inclusions system
• iterative method
• krasnoselskii’s theorem
• a-contraction
• matrix convergent to zero
• multivalued operator
• perov’s theorem
• relatively compact operator
• sum of two operators
• vector-valued metric
• vector-valued norm
• fredholm-volterra type inclusions system
• primary 47h10, 54h25