FUNCTIONAL EQUATIONS RELATED TO GP MAPPINGS OF DEGREE AT MOST N

Abstract

Let V and W be real vector spaces, in this paper, we prove that a mapping f : V → W satises a specic functional equation (1.1) if and only if there exist mappings f_1, f_2, ⋯, f_n : V → W satisfying f(x) = \sum_{k=1}^{n} and f_k(x) and f_k(ax) = a_k f_k(x) for all x∈V and k∈{1, 2, ⋯, n} where a is a real number with a < 1 and 0 < a_1 < a_2 < ⋯ < a_n