Investigations on the Hyers–Ulam stability of generalized radical functional equations

Abstract

In (Brzdęk and Schwaiger in Aeq Math 92: 975-991, 2018) solutions of far reaching generalizations of the so-called radical functional equation f (p(π(x) + π(y))) = f (x) + f (y) have been investigated. These investigations are continued here by analysing the corresponding stability results, which have been the main subject of several recent papers. We propose a very general and uniform approach.

Ulam‐Hyers‐Rassias stability for generalized fractional differential equations

“…Since then numerous articles have been published on this subject and we refer to previous works 19–24 for more details.…”

On Hyers-Ulam-Rassias stability of fractional differential equations with Caputo derivative

“…The legendary question that has been posed by Ulam in 1940 ignited the theory of stability of functional (differential, difference, integral) equations. Ulam posed his question in the famous talk at the university of Wisconsin (see, e.g., [9,13,16,18,28,31] for more details). The mentioned open problem can be stated as follows:…”