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Title: A note on functional equations connected with the Cauchy mean value theorem
Authors: Łukasik, Radosław
Keywords: Functional equation; Linearly dependent functions; Mean value theorem
Issue Date: 2018
Citation: Aequationes Mathematicae, Vol. 92, no. 5 (2018), s. 935-947
Abstract: The aim of this paper is to describe the solution (f, g) of the equation [f(x)-f(y)]g′(αx+(1-α)y)=[g(x)-g(y)]f′(αx+(1-α)y),x,y∈I,where I⊂ R is an open interval, f, g: I→ R are differentiable, α is a fixed number from (0, 1).
DOI: 10.1007/s00010-018-0583-2
ISSN: 0001-9054
Appears in Collections:Artykuły (WMFiCH)

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