A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution

Ulam-Hyers stability of a 2-variable AC-mixed type functional equation in Felbin's type spaces: fixed point method

“…This stability problem was further generalized by several authors [2,9,28,32,36]. We cite also other pertinent research works [1,4,7,11,15,16,18,31,33,37,40,46,48].…”

Solution of the Ulam stability problem for Euler-Lagrange-Jensen k-cubic mappings

“…Since then various "cubic" equations have been proposed and solved by a number of experts in the area of functional equations and inequalities (see also [4,7,19,23,25,32,35,38,[40][41][42]). For further research in various normed spaces, we are introducing new cubic functional equations, and establish fundamental formulas for the general solution of such functional equations and for the "Ulam stability" of pertinent cubic functional inequalities.…”

A fixed points approach to stability of the Pexider equation

“…If we set K = {I, σ}, were I: E −→ E denotes the identity function and σ denote an additive function of E, such that σ(σ(x)) = x, for all x ∈ E then equation (1.1) reduces to the Pexider functionals equations Cǎdariu and V. Radu [9] notice that a fixed point alternative method is very important for the solution of the Hyers-Ulam stability problem. Subsequently, this method was applied to investigate the Hyers-Ulam-Rassias stability for Jensen functional equation, as well as for the additive Cauchy functional equation [12] by considering a general control function ϕ(x, y), with suitable properties, using such an elegant idea, several authors applied the method to investigate the stability of some functional equations, see for example [3], [4], [5], [6], [31], [35], [43].…”