Stability of n-Dimensional Additive Functional Equation in Generalized 2-Normed Space

Abstract

Abstract. In this paper, the author established the general solution and generalized Ulam-Hyers-Rassias stability of n-dimensional additive functional equationin generalized 2-normed space.

Stability of system of additive functional equations in various Banach spaces: Classical Hyers methods

“…Lee [27], K. Ravi, M. Arunkumar [33], M. Arunkumar [4,5,7,8,11]. In this paper, authors proved the generalized Ulam -Hyers stability of system of additive functional equations…”

On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey II

“…In this paper, we complement the content of [23], where the (less complicated) results from [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] have been surveyed. Here, we present and discuss the (more involved) outcomes on Ulam stability in 2-normed spaces provided in [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Stability of a Functional equation originating from sum of first l natural numbers in Intuitionistic Fuzzy Banach Space and Algebras using Direct and Fixed Point Methods

“…Lee [25], K. Ravi, M. Arunkumar [46], M. Arunkumar [3,4,5,6,7,10], J. M. Rassias et.al., [43]. The generalized Ulam -Hyers stability of several functional equations in various Banach spaces including Intuitionistic Fuzzy Banach spaces and Algebras were investigated in [8,9,11,12,15,16,17,18,19,21,13,14,43].…”

“…11 If W : M 1 → M 2 is a function satisfying the inequalities(39) and (59) for all w 1 , w 2 . • • • , w ∈ M 1 and all η > 0, with positive numbers a > 0 and b = 1, 1 .…”