Invariance of quasi-arithmetic means with function weights

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:353

Article

Jarczyk, Justyna

关键词: Mean;    Functional equation;    Invariant mean;    Quasi-arithmetic mean;    Function weight;   

DOI  :  10.1016/j.jmaa.2008.11.046

来源: Elsevier

【 摘 要 】

Let I subset of R be a non-trivial interval and let lambda, mu, nu: I(2) -> (0, 1). We present some results concerning the following functional equation, generalizing the Matkowski-Suto equation, lambda(x, y)phi(-1) (mu(x, y)phi(x) + (1 - mu(x, y))phi(y)) + (1 - lambda(x, y))phi(-1), (nu(x, y)psi(x) + (1 - nu(x, y))psi(y)) = lambda(x, y)x + (1 - lambda(x, y))y, where phi, psi : I -> R are continuous and strictly monotonic unknown functions. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free