On a functional equation containing four weighted arithmetic means
نویسندگان
چکیده
منابع مشابه
On a Functional Equation Containing Four Weighted Arithmetic Means
In this paper we solve the functional equation f ( αx+ (1− α)y ) + f ( βx+ (1− β)y ) = f ( γx+ (1− γ)y ) + f ( δx+ (1− δ)y ) which holds for all x, y ∈ I, where I ⊂ R is a non-void open interval, f : I → R is an unknown function and α, β, γ, δ ∈ (0, 1) are arbitrarily fixed.
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Let P denote the collection of positive sequences defined on N. Fix w ∈ P. Let s, t, respectively, be the sequences of partial sums of the infinite series ∑ wk and ∑ sk, respectively. Given x ∈ P, define the sequences A(x) and G(x) of weighted arithmetic and geometric means of x by An(x) = n ∑ k=1 wk sn xk, Gn(x) = n ∏ k=1 x wk/sn k , n = 1, 2, . . . Under the assumption that log t is concave, ...
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ژورنال
عنوان ژورنال: Banach Journal of Mathematical Analysis
سال: 2008
ISSN: 1735-8787
DOI: 10.15352/bjma/1240336269