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Monotony conditions

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December 13, 2019
functionmonotonyalgebra

Problem Statement

Consider a function f:R⟶R. f:\mathbb{R}\longrightarrow\mathbb{R} . Show that:
a) f f is nondecreasing, if f+g f+g is nondecreasing for any increasing function g:R⟶R. g:\mathbb{R}\longrightarrow\mathbb{R} .
b) f f is nondecreasing, if f⋅g f\cdot g is nondecreasing for any increasing function g:R⟶R. g:\mathbb{R}\longrightarrow\mathbb{R} .
Cristian Mangra
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