ON THE SPACE OF (phi, gamma)-PSEUDO-JENSEN MAPPINGS ON GROUPS

Abstract

In this paper the generalized Hyers-Ulam-Rassias type stability of the Jensen equation on some classes of groups is established. It is shown that the Jensen equation is stable on any metabelian group. It is also proved that every group can be embedded to a group in which the Jensen equation is stable. Many of the results in this paper are generalization of the results of an earlier paper of the authors [V. A. Faiziev and P. K. Sahoo, On the space of pseudo-jensen functions on groups, St. Petersburg Math. J., 14 (2003), 1043-1065].