General actions of hyperstructures and some applications

Abstract

The aim of this paper is to investigate useful generalizations of the classical concept of a quasi-automaton without outputs or a discrete dynamical system, which are also called actions of semigroups or groups on given phase sets. The paper contains also certain applications of presented concepts and examples from various areas of mathematics.

Keywords

• action of a hyperstructure on a set
• general n-hyperstructure
• transformation hypergroup
• fredholm integral operator
• ordinary and partial differential operator