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ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

신동윤|이정례|윤성식
한국수학교육학회|2016.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제23권 제3호|pp. 247-263

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참고문헌

키워드

fuzzy Banach spaceadditive–quadratic ρ–functional inequalityHyers– Ulam stability References
주제분류수학

초록

M_1f(x,y) : & = & \frac{3}{4} f(x+y) - \frac{1}{4}f(-x-y) + \frac{1}{4} f(x-y) + \frac{1}{4} f(y-x) - f(x) - f(y),\\ M_2 f(x,y): &= &2 f\left( \frac{x+y}{2} \right) + f\left( \frac{x-y}{2}\right) + f\left( \frac{y-x}{2}\right) - f(x) - f(y). Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic $\rho$-functional inequalities N(M_1f(x,y),t) \ge N\left(\rho M_2 f(x,y), t \right) where $\rho$ is a fixed real number with $|\rho|<1$, and N\left(M_2f(x,y),t\right) \ge N\left(\rho M_1f(x,y),t\right) where $\rho$ is a fixed real number with $|\rho|<\frac{1}{2}$.

Abstract

M_1f(x,y) : & = & \frac{3}{4} f(x+y) - \frac{1}{4}f(-x-y) + \frac{1}{4} f(x-y) + \frac{1}{4} f(y-x) - f(x) - f(y),\\ M_2 f(x,y): &= &2 f\left( \frac{x+y}{2} \right) + f\left( \frac{x-y}{2}\right) + f\left( \frac{y-x}{2}\right) - f(x) - f(y). Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic $\rho$-functional inequalities N(M_1f(x,y),t) \ge N\left(\rho M_2 f(x,y), t \right) where $\rho$ is a fixed real number with $|\rho|<1$, and N\left(M_2f(x,y),t\right) \ge N\left(\rho M_1f(x,y),t\right) where $\rho$ is a fixed real number with $|\rho|<\frac{1}{2}$.

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