# General Solution and Generalized Hyers-Ulam Stability of n-dimensional Cubic Functional Equation in Various Normed Space: Direct and Fixed Point Methods

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## Keywords:

Cubic functional equations, FNS, RNS, IFNS, FELBIN'S type spaces, fixed point, generalized Hyers-Ulam Stability## Abstract

In this paper, the authors investigate the general solution in vectors space and generalized Hyers-Ulam Stability of n-dimensional Cubic functional Equation

$$f\left(\sum^{n}_{i=1}{x_{i}}\right)+\sum^{n}_{j=1}f\left(-x_{j}+\sum_{i=1;i\neq j}{x_{i}}\right)=\left(n-5\right)\sum_{ 1\leq i<j\leq k\leq n }f\left({{x_{i}+x_{j}+x_{k}}}\right)$$

$$+\left(-n^{2}+8n-11\right)\sum_{i=1;i\neq j}{f\left(x_{i}+x_{j}\right)-\sum^{n}_{j=1}{f\left({2x_{j}}\right)}}$$ $$+\frac{1}{2}\left(n^{3}-10n^{2}+23n+2\right)\sum^{n}_{i=1}f\left({x_{i}}\right)$$

with $n>5$, and n is a positive integer using FNS,RNS,IFNS and FELBIN'S type spaces, using direct and fixed point methods.

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*International Journal of Mathematics And Its Applications*,

*4*(1 - D), 81–109. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/395

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Copyright (c) 2016 International Journal of Mathematics And its Applications

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