STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES

Abstract

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality ∥f (x1 +x2)+f (x2 +x3)+· · ·+f (xn +x1)∥ ≤ ∥tf (x1 +x2 +· · ·+xn)∥ in Banach spaces where a positive integer n ≥ 3 and a real number t such that 2 ≤ t < n.

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