On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions

Stability of the Popoviciu type functional equations on groups

“…Stability of (1.3) has been investigated by S.-M. Jung [5] and W. Fechner [4]. Solutions and stability of some further generalization of (1.1) have been investigated by T. Trif [11]. In [3] the general solution of the following functional equation…”

Decomposable functions and representations of topological semigroups

“…and problems of their stability have been studied by many authors (see [2,3,5,10,11]). The main result of this paper is that for a wide class of semigroups G (including all topologically finitely generated semigroups), a continuous function f , satisfying (3), is a matrix element of a finite-dimensional continuous representation of G. In this case each function u E j (and v E j ) can be chosen as a product of functions of one argument.…”

A Fixed Point Approach to the Cauchy-Rassias Stability of General Jensen Type Quadratic-Quadratic Mappings

“…Also, Trif [28] studied the Cauchy-Rassias stability of the Jensen type functional equation. In addition, Park [17] studied the Cauchy-Rassias stability of modified Trif functional equations associated with homomorphisms in Banach module over C*-algebras.…”