Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation

On functions that are approximate fixed points almost everywhere and Ulam’s type stability

“…Corollary 2.5 yields at once the following two outcomes that generalize (at least to some extent) several results in [1,2,5,7,8,13,18,19].…”

Fixed-point results and the Hyers–Ulam stability of linear equations of higher orders

“…In this paper we describe (in the terms of fixed points) a general method for investigation of the Hyers-Ulam stability of various higher-order linear (differential, integral, difference or functional) equations in a single variable, that is, for n = 1. In this way we show how to generalize and easily extend numerous results given in, e.g., [Takahasi et al 2002;Miura et al 2003a;2003b;Popa 2005b;Trif 2006;Wang et al 2008;Brzdȩk et al 2008;2011b;Li and Shen 2009;Brzdȩk and Jung 2010].…”

“…Equation 14is a discrete case of (15); its Hyers-Ulam stability was discussed in [Popa 2005a;2005b;Brzdȩk et al 2006;. Equation 15is one of the most important functional equations, and many results on its solutions can be found in [Kuczma 1968;Kuczma et al 1990] (see also the references therein); its Hyers-Ulam stability was discussed, e.g., in [Kim 2000;Trif 2002] for m = 1 and in [Trif 2006;Brzdȩk et al 2008;2011b;Brzdȩk and Jung 2010] for m > 1.…”

On approximate solutions of the linear functional equation of higher order

“…The Hyers-Ulam stability of Eq. (1) has been investigated so far mainly for m = 1 and, except some results in [8,10,31,36] concerning the case where the coefficient functions a 1 , . .…”