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STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES

신동윤|윤성식
한국수학교육학회|2017.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제24권 제1호|pp. 21-31|DOI https://doi.org/10.7468/jksmeb.2017.24.1.21

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키워드

direct methodHyers-Ulam stabilityfixed point methodadditive (ρ1ρ2)-functional inequalityBanach space.
주제분류수학

초록

In this paper, we introduce and solve the following additive (rho_1, rho_2)-functional inequality $$ \left\|2 f\left(\frac{x+y}{2}\right) - f(x )-f(y)\right\| \le \|\rho_1 (f(x+y)+ f(x-y)-2f(x))\|$$ $$ + \left\|\rho_2 \left( f(x+y)-f(x)-f(y)\right)\right\| ,$$where $\rho_1$ and $\rho_2$ are fixed nonzero complex numbers with $\sqrt{2} |\rho_1|+ |\rho_2| <1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (rho_1, rho_2)-functional inequality in complex Banach spaces.

Abstract

In this paper, we introduce and solve the following additive (rho_1, rho_2)-functional inequality $$ \left\|2 f\left(\frac{x+y}{2}\right) - f(x )-f(y)\right\| \le \|\rho_1 (f(x+y)+ f(x-y)-2f(x))\|$$ $$ + \left\|\rho_2 \left( f(x+y)-f(x)-f(y)\right)\right\| ,$$where $\rho_1$ and $\rho_2$ are fixed nonzero complex numbers with $\sqrt{2} |\rho_1|+ |\rho_2| <1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (rho_1, rho_2)-functional inequality in complex Banach spaces.

참고문헌 (31)

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