MathDB
Miklos Schweitzer 1981_6

Source:

January 29, 2009
functioninequalitiestrigonometryintegrationreal analysisreal analysis unsolved

Problem Statement

Let f f be a strictly increasing, continuous function mapping I=[0,1] I=[0,1] onto itself. Prove that the following inequality holds for all pairs x,y∈I x,y \in I: 1−cos⁡(xy)≤∫0xf(t)sin⁡(tf(t))dt+∫0yf−1(t)sin⁡(tf−1(t))dt. 1-\cos (xy) \leq \int_0^xf(t) \sin (tf(t))dt + \int_0^y f^{-1}(t) \sin (tf^{-1}(t)) dt . Zs. Pales
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