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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.
Said R. Grace,Sandra Pinelas 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.2
We establish several growth theorems for second order nonlinear differential and integro-differential equations. We also give necessary and suffcient conditions for solutions of second order non-linear differential equations to be bounded together with their frst derivatives and investigate its asymptotic behavior.
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.
STABILITY OF A SEXVIGINTIC FUNCTIONAL EQUATION
Lee Jung Rye,Park Choonkil,Pinelas Sandra,Govindan Viya,Tamilvanan K.,Kokila G. 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.2
In this paper, we estabilish the general solution of sexvigintic functional equation f (x + 13y) − 26f (x + 12y) + 325f (x + 11y) − 2600f (x + 10y) + 14950f (x + 9y)−65780f (x + 8y) + 230230f (x + 7y) − 657800f (x + 6y) + 1562275f (x + 5y)−3124550f (x + 4y) + 5311735f (x + 3y) − 7726160f (x + 2y) + 9657700f (x + y)−10400600f (x) + 9657700f (x − y) − 7726160f (x − 2y) + 5311735f (x − 3y)−3124550f (x − 4y) + 1562275f (x − 5y) − 657800f (x − 6y) + 230230f (x − 7y)−65780f (x − 8y) + 14950f (x − 9y) − 2600f (x − 10y) + 325f (x − 11y)−26f(x − 12y) + f (x − 13y) = 26!f(y) and investigate the Hyers-Ulam stability of this functional equation in Banach spaces using two different methods.