Abstract
Let 0 ⩽e < 1 and letX, Y be real normed spaces. In this paper we consider the following functional inequality:∥f(x + y) − f(x) − f(y)∥ ⩽ e min{∥f(x + y)∥, ∥f(x) + f(y)∥} forx, y ∈ R, wheref: X → Y. Mainly continuous solutions are investigated. In the case whereY = R some necessary and some sufficient conditions for this inequality are given.
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