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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.
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참고문헌 (27)
참고문헌 신청
A. Chahbi / 2013 / On the generalized stability of d'Alembert functional equa-tion / J. Nonlinear Sci. Appl 6 : 198 ~ 204
C. Park / 2007 / Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras / Fixed Point Theory Appl 2007
C. Park / 2008 / Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach / Fixed Point Theory Appl 2008
C. Park / 2012 / Orthogonal stability of a cubic-quartic functional equation / J. Nonlinear Sci. Appl 5 : 28 ~ 36
C. Park / 2013 / Approximate n-Jordan *-homomorphisms in C*-algebras / J. Comput. Anal. Appl 15 : 365 ~ 368
C. Park / 2007 / Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras / Fixed Point Theory Appl 2007
C. Park / 2008 / Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach / Fixed Point Theory Appl 2008
C. Park / 2012 / Orthogonal stability of a cubic-quartic functional equation / J. Nonlinear Sci. Appl 5 : 28 ~ 36
C. Park / 2013 / Approximate n-Jordan *-homomorphisms in C*-algebras / J. Comput. Anal. Appl 15 : 365 ~ 368
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