The properties of functional inclusions and Hyers–Ulam stability

Abstract

Abstract. We prove that a set-valued function satisfying some functional inclusions admits, in appropriate conditions, a unique selection satisfying the corresponding functional equation. As a consequence we obtain the result on the Hyers-Ulam stability of that functional equation.Mathematics Subject Classification (2010). 39B05, 39B82, 54C60, 54C65.

On Selections of Set-Valued Inclusions in a Single Variable with Applications to Several Variables

“…The subsequent theorem is a simple modification of Theorem 1 in [12]. However, we prove it for the convenience of the readers.…”

“…The aim of this paper is to give some modification of Theorem 1 in [12] and its applications. We also show that our theorem generalizes the above results.…”

Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability

“…The next simple theorems show some direct applications of Theorem 1; they correspond to the results on stability of functional equations (for the setvalued mappings) in [6][7][8][9][10]. Then, it is easily seen that it is i.p.…”

On Characterizations of Set-Valued Dynamics

“…M. Rassias and J. Tabor. In [17,18], Piszczek obtained some results of stabilities of functional equations in some classes of multi-valued functions. Chu et al [6] also investigated the Hyers-Ulam stability of the n-dimensional cubic set-valued functional equation…”