On the Hyers–Ulam Stability of the Functional Equations That Have the Quadratic Property

Abstract

Ž .The Hyers᎐Ulam stability of the quadratic functional equation 1 on a restricted domain shall be investigated, and the result shall be applied to the study of an asymptotic behavior of that equation. Furthermore, the Hyers᎐Ulam stability Ž . Ž . problems of another quadratic equation 4 on a restricted domain shall also be Ž . treated under the approximately even or odd condition, and some asymptotic behaviors of the quadratic mappings and the additive mappings shall be investigated. ᮊ 1998 Academic Press

Stability of a generalization of the Fréchet functional equation

“…The results we prove correspond also to some outcomes in [8,11,16,19,25]. The results in [2] as well as our main theorem have been motivated by the notion of hyperstability of functional equations (see, e.g., [3,4,5,13,20]), introduced in connection with the issue of stability of functional equations (for more details see, e.g., [14,17]).…”

On the generalized Fréchet functional equation with constant coefficients and its stability

“…Such a method has been used in, e.g., [4][5][6]10,26,30,33,34]. Moreover, the results that we provide correspond to the outcomes in [3,9,13,16,18,21,24,25,31,32] (for more details see, e.g., [8,19,22]) and complement [4,Corollary 6]. …”

Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

“…One of the most relaxed methods for stability for functional equations was introduced by Ulam [24] and Hyers [25] which is known as Hyers-Ulam stability. The aforesaid stability has been very well investigated for ordinary differential and integral equations as well as functional equations; see [26][27][28][29]. But for FODEs, the concerned stability is not properly investigated.…”