Approximate derivations on Banach algebras associated with Jensen functional equation

Abstract

In this paper, we examine the generalized Hyers–Ulam stability of derivations associated with the Jensen functional equation f ( x − y n + z ) + f ( y − z n + x ) + f ( z − x n + y ) = f(x) + f(y) + f(z) on Banach algebras for any fixed nonzero integer n. Mathematics Subject Classification: 45J05; 46B03 This work was supported by the Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2012R1A1A2008139 and No. 2012-0002410). 1784 I. Chang and H. Kim