ADDITIVE rho-FUNCTIONAL INEQUALITIES AND EQUATIONS

作者：Park Choonkil^*

来源：Journal of Mathematical Inequalities, 2015, 9(1): 17-26.

DOI：10.7153/jmi-09-02

• Hyers-Ulam stability
• additive rho-functional equation
• additive rho-functional inequality

In this paper, we investigate the additive rho-functional inequalities
parallel to f(Sigma(k)(j=1)xj) - Sigma(k)(j=1)f(xj)parallel to <=parallel to rho(kf(Sigma(k)(j=1)xj/k) - Sigma(k)(j=1)f(xj)parallel to (0.1)
and
parallel to kf(Sigma(k)(j=1)xj/k - Sigma(k)(j=1)f(xj)parallel to <=parallel to rho(f(Sigma(k)(j=1)xj) - Sigma(k)(j=1)f(xj)parallel to, (0,2)
where rho is a fixed complex number with vertical bar rho vertical bar < 1.
Furthermore, we prove the Hyers-Ulam stability of the additive rho-functional inequalities (0.1) and (0.2) in complex Banach spaces and prove the Hyers-Ulam stability of additive rho-functional equations associated with the additive rho-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• 出版日期2015-3