Eine zur Parallelogrammgleichung äquivalente Ungleichung

Abstract

Abstract. Characterizations of pairs of stochastic processes that can be separated by Jensen and by affine stochastic processes are presented. As a consequence, some stability results of the Hyers-Ulam-type are obtained.Mathematics Subject Classification. Primary 26A51, Secondary 39B62, 60G99.

On functional inequalities associated with Drygas functional equation

“…In the proof we use Gy. Maksa and Volkmann's [13] and Gilányi [9] results to prove that f e is a solution of the quadratic functional equation (1.2) and f o is a solution of the Cauchy functional equation. Writing x = y = 0 in (2.1), we obtain 3 f (0) ≤ f (0) , so f (0) = 0.…”

Additive ρ --functional inequalities

“…See [2,3,4,13] for more information on functional equations. In [8], Gilányi showed that if f satisfies the functional inequality…”

The stability of quadratic α -functional equations

“…A generalization of the Rassias theorem was obtained by Gȃvruta [10] by replacing the unbounded Cauchy difference by a general control function in the spirit of Rassias' approach. See [2,3,7,9,11,12,18] for more information on functional equations.…”