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2022•Journal of Advances in Mathematics and Computer ScienceOpen access

Hyers-Ulam-Rassias Stability of a General Septic Functional Equation

Sun-Sook Jin, Yang-Hi Lee

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Abstract

In this paper, we investigate the stability of the following general septic functional equation: \(\sum_{i=0}^8{ }_8 C_i(-1)^{8-i} f(x+(i-4) y)=0\)which is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation, the quintic functional equation, and the sextic functional equation. The equation is analysed from the perspective of Hyers-Ulam-Rassias stability.

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What this paper is about

In this paper, we investigate the stability of the following general septic functional equation: \(\sum_{i=0}^8{ }_8 C_i(-1)^{8-i} f(x+(i-4) y)=0\)which is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation, the quintic functional equation, and the sextic functional equation. The equation is analysed from the perspective of Hyers-Ulam-Rassias stability.

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Available abstract

In this paper, we investigate the stability of the following general septic functional equation: \(\sum_{i=0}^8{ }_8 C_i(-1)^{8-i} f(x+(i-4) y)=0\)which is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation, the quintic functional equation, and the sextic functional equation. The equation is analysed from the perspective of Hyers-Ulam-Rassias stability.

Key concepts: Functional equation, Mathematics, Stability (learning theory), Generalization, Quartic function, Quintic function, Quadratic equation, Mathematical analysis

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