Some Fixed Point Properties of Self-Maps Constructed by Switched Sets of Primary Self-Maps on Normed Linear Spaces

Abstract

This paper is devoted to the investigation of the existence of fixed points in a normed linear space X endowed with a norm ‖⋅‖ for self-maps f from T×X to X which are constructed from a given class of so-called primary self- maps being also from T×X to X. The construction of the self-maps of interest is performed via a so-called switching rule which is a piecewise-constant map from a set T to some finite subset of the positive integers or a sequence map which domain in some discrete subset of T