Stability of a general p-radical functional equation related to additive mappings in 2-Banach spaces

Abstract

In this paper, we introduce and solve a new general p-radical functional equation Also, we investigate some stability and hyperstability results for the considered equation in 2-Banach spaces. In addition, we prove the hyperstability of the inhomogeneous p-radical functional equation

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

“…In Theorem 3.2 of [46], the authors obtained an outcome that is similar to Theorem 12 and reads as follows.…”

“…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.…”

“…for functions F : R → Y, where p, k ∈ N \ {1} are fixed. The first main stability result in Theorem 3.1 of [46] reads as follows (some typos made in [46] have been corrected).…”

“…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 Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey

“…Several other stability results in 2-normed spaces (also non-Archimedean and random) have been presented in [65] (for the Pexiderized Cauchy functional equation), in [17,66] (for the Cauchy equation), in [67] (for a generalized radical cubic functional equation related to quadratic functional equation), in [68] (for the radical quartic functional equation), in [69] (for the quadratic functional equation), in [70] (for the generalized Cauchy functional equation), in [71] (for a functional equation called the Cauchy-Jensen functional equation), in [72] (for a general p-radical functional equation) [73] (for radical sextic functional equation), in [74] (for several functional equations of quadratic-type), in [75,76] (for the functional equation of p-Wright affine functions), in [77] (for a system of additive-cubicquartic functional equations with constant coefficients in non-Archimedean 2-normed spaces), in [78] (for a functional inequality in non-Archimedean 2-normed spaces), in [79] (for a cubic functional equation in random 2-normed spaces), in [80] (for the Pexiderized quadratic functional equation in the random 2-normed spaces) and in [81] (for radical functional equations in 2-normed spaces and p-2-normed spaces). However, as these results are more involved and of a different character than those presented so far, we will discuss them in more details in another publication.…”