On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations

Abstract

In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n-dimensional functional equation: f (We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.

Ulam stability of a generalized reciprocal type functional equation in non-Archimedean fields

“…This type of stability involving a product of powers of norms is called Ulam-Gavruta-Rassias Stability by Bouikhalene and Elquorachi [3], Nakmahachalasint [17,18], Park and Najati [19], Pietrzyk [20] and Sibaha et al [30].…”

On the Ulam stability of an n-dimensional quadratic functional equation

“…Later, Bae and Park [2] and Nakmahachalasint [12] considered the Ulam stability of another n-dimensional quadratic functional equation…”

On the Generalized Hyers-Ulam Stability of ann-Dimensional Quadratic and Additive Type Functional Equation

“…. , ∈ ( > 2) (see also [11][12][13][14][15]). The functional equation (2) is a quadratic-additive type functional equation (see Theorem 2.6 in [16]).…”