On a concave differentiable majorant of a modulus of continuity. (English) Zbl 1012.26003

Medvedev, A. V.

Real Anal. Exch. 27(2001-2002), No. 1, 123-129 (2002).

Summary: We prove that for any modulus of continuity on \([0,\infty)\) there exists a concave majorant that is infinitely differentiable on \((0,\infty)\) and satisfies an additional inequality. This extends the results of Stechkin and Kornejchuk obtained previously without the requirement that majorants be differentiable.

MSC:

26A15

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable

Keywords:

modulus of continuity; concave majorant