Journal of Inequalities & Applications, Dec 2013, 2013(1), p1-10. 10p.
Abstract
We prove the Hyers-Ulam stability of the Cauchy functional inequality and the Cauchy-Jensen functional inequality in 2-Banach spaces. Moreover, we prove the superstability of the Cauchy functional inequality and the Cauchy-Jensen functional inequality in 2-Banach spaces under some conditions.