Stability of a Monomial Functional Equation on a Restricted Domain

Abstract

Abstract:In this paper, we prove the stability of the following functional equation ∑ n i=0 n C i (−1) n−i f (ix + y) − n! f (x) = 0 on a restricted domain by employing the direct method in the sense of Hyers.

Generalized Hyers-Ulam Stability of the Pexider Functional Equation

“…satisfying inequality (14) and f satisfies inequality (13) for all x, y, z, w ∈ V. Then, there exists a unique additive mapping F :…”

Bi-Additive s-Functional Inequalities and Quasi-∗-Multipliers on Banach Algebras

“…Let r > 2 and θ be nonnegative real numbers, and let f : A 2 → A be a mapping satisfying (24) and f (x, 0) = f (0, z) = 0 for all x, z ∈ A. Then there exists a unique bi-additive mapping B : A 2 → A, which is C-linear in the first variable and satisfies (25).…”

“…Then for each given element x ∈ X, either d(J n x, J n+1 x) = ∞ for all nonnegative integers n or there exists a positive integer n 0 such that (1) d(J n x, J n+1 x) < ∞, ∀n ≥ n 0 ; (2) the sequence {J n x} converges to a fixed point y * of J; (3) y * is the unique fixed point of J in the set Y = {y ∈ X | d(J n 0 x, y) < ∞}; (4) d(y, y * ) ≤ In 1996, Isac and Rassias [20] were the first to provide applications of stability theory of functional equations for the proof of new fixed point theorems with applications. By using fixed point methods, the stability problems of several functional equations have been extensively investigated by a number of authors (see [21][22][23][24][25]). This paper is organized as follows: In Sections 2 and 3, we prove the Hyers-Ulam stability of the following bi-additive s-functional inequalities…”

C*-Ternary Biderivations and C*-Ternary Bihomomorphisms

“…The stability problems of various functional equations and functional inequalities have been extensively investigated by a number of authors (see [12][13][14][15][16][17][18][19][20]). …”