On the stability of a sum form functional equation related to entropies of type (α,β)

Abstract

In this paper, we discuss the stability of the sum form functional equation n ∑ i=1 m ∑ j=1 f(piqj) = n ∑ i=1 g(pi) m ∑ j=1 f(qj) + n ∑ i=1 f(pi) m ∑ j=1 q β j for all complete probability distributions (p1, . . . ,pn) ∈ Γn, (q1, . . . ,qm) ∈ Γm, n > 3, m > 3 are fixed integers, f, g are real valued mappings each having the domain I = [0, 1] and β is a fixed positive real power such that β 6= 1, 0β := 0, 1β := 1.