ON APPROXIMATION OF THE PERTURBED INCLUSION

Abstract. The paper is concerned with the so-called perturbed inclusion in the space of continuous functions. The right-hand side of the inclusion is represented by an algebraic sum of the values of two multi-valued maps, one of which consists of compacts and the other is not necessarily closed-valued and is a composition of a linear integral operator and multimap convex-valued with respect to switching. For such an inclusion it is proved that approximation in the space of summable functions of the values of a multimap convex-valued with respect to switching is not always a stable process. The necessary and sufficient condition for the closure of the set of approximate solutions to converge to the closure of the set of solutions for perturbed inclusion is derived. 2000 Mathematics Subject Classification: 34A60, 45G15, 47H04. Key words and phrases: Asymptotic representation of the solutions sets for inclusions. The perturbed inclusion with external perturbations has already been studie