On the asymptoticity aspect of Hyers-Ulam stability of mappings

Abstract

Abstract. The object of the present paper is to prove an asymptotic analogue of Th. M. Rassias' theorem obtained in 1978 for the Hyers-Ulam stability of mappings.

Approximately Quadratic Mappings on Restricted Domains

“…Indeed, for the case r = s = 1 2 in (1.2), we get (1.1). In 1983 Skof [38] was the first author to solve the Hyers-Ulam problem for additive mappings on a restricted domain (see also [13], [20] and [23]). In 1998 Jung [19] investigated the Hyers-Ulam stability for additive and quadratic mappings on restricted domains (see also [21], [24] and [25]).…”

On the integral functional equations: On the integral d'Alembert's and Wilson's functional equations

“…In Corollaries 4.3 and 4.4 we give explicit formulas of solutions of (1.2) and (1.8) in terms of irreducible representations of G. Theses formulas generalize Euler's formula cos(x) = e ix +e −ix 2 on G = R. In the last section we study stability [48] and Baker's superstability (see [5] and [6]) of the functional equations (1.1), (1.2), (1.3), (1.4), (1.5), (1.6) and (1.7). For more information concerning the stability problem we refer to [3], [5], [6], [11], [12], [22], [40], [41], [42], [43], [44], [45], [46], [47] and [48]. The results of the last sections generalize the ones obtained in [12] and [21].…”

On Some New Multivalued Results in the Metric Spaces of Perov’s Type

“…About of weakly Picard operators see example [12,13]. Also, for Ulam stability of some functional equations see [11,[14][15][16][17][18][19][20].…”