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Solution and stability of an $n$-variable additive functional equation
Vediyappan Govindan,이정례,Sandra Pinelas,Abdul Rahim Noorsaba,Ganapathy Balasubramanian 강원경기수학회 2020 한국수학논문집 Vol.28 No.3
In this paper, we investigate the general solution and the Hyers-Ulam stability of $n$-variable additive functional equation of the form $$\Im\left(\sum_{i=1}^{n}(-1)^{i+1}x_i\right)=\sum_{i=1}^{n}(-1)^{i+1}\Im (x_i),$$ where $n$ is a positive integer with $n \ge 2$, in Banach spaces by using the direct method.
Stability of -variable Additive and -variable Quadratic Functional Equations
Vediyappan Govindan,Sandra Pinelas,이정례 한국수학교육학회 2022 純粹 및 應用數學 Vol.29 No.2
In this paper we investigate the Hyers-Ulam stability of the s-variable additive and -variable quadratic functional equations of the form f(sum _{i=1} ^{s}{x}{i})+ sum _{j=1} ^{s}{f}(-{s}{x}{j}+sum _{i=1,i≠j} ^{s}{x}{i})=0 and f( sum _{i=1} ^{l} {x}{i} )+ sum _{j=1} ^{l} f(-{l}{x}{j}+ sum _{i=1,i != j} ^{l} {x}{i})=(l+1) sum _{i=1,i != j} ^{l} f({x}{i} -{x}{j})+(l+1) sum _{i=1} ^{l} f({x}{i}) (s, ∈N, s, ≥3)in qusai-Banach spaces.
GENERAL SOLUTION AND ULAM STABILITY OF GENERALIZED CQ FUNCTIONAL EQUATION
Govindan, Vediyappan,Lee, Jung Rye,Pinelas, Sandra,Muniyappan, P. The Kangwon-Kyungki Mathematical Society 2022 한국수학논문집 Vol.30 No.2
In this paper, we introduce the following cubic-quartic functional equation of the form $$f(x+4y)+f(x-4y)=16[f(x+y)+f(x-y)]{\pm}30f(-x)+\frac{5}{2}[f(4y)-64f(y)]$$. Further, we investigate the general solution and the Ulam stability for the above functional equation in non-Archimedean spaces by using the direct method.