Stability of quartic functional equations in 2-Banach space

Abstract

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation f (2x + y) + f (2x − y) = 4f (x + y) + 4f (x − y) + 24f (x) − 6f (y) in 2-Banach space.

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

“…In this paper, we have presented and discussed the results on Ulam stability in 2normed spaces provided in articles [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. In this way, we complement the paper [23], where the results from [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] have been surveyed. We have shown how to supplement or improve several of these results.…”

“…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].…”

On the stability problem of quadratic functional equations in 2-Banach spaces

“…Recently, many mathematicians came out with results in linear 2-normed spaces, analogous with that in classical normed spaces and Banach spaces. In particular, the stability problems of the functional equations in 2-normed spaces have investigated by [1,3,11,12]. Before we present our results, we introduce some basic facts concerning linear 2-normed spaces.…”

On the Hyers-Ulam stabilities of functional equations on n-Banach spaces

“…By a direct method of fixed points, Kenary et al. obtained the generalized Hyers–Ulam stability for a quadratic functional equation The generalized Hyers–Ulam stability for several functional equations in 2‐Banach spaces was investigated by Park , , while Patel et al . studied the Hyers–Ulam stability of the functional equation in 2‐Banach space.…”

“…The generalized Hyers-Ulam stability for several functional equations in 2-Banach spaces was investigated by Park [10], [18], while Patel et al [19] studied the Hyers-Ulam stability of the functional equation…”