On the second moduli of continuity
We prove an inequality for the second moduli of continuity of continuous functions. Applying this inequality, we construct a nonnegative nonincreasing continuous function ω on [0, +g8) that vanishes at zero and is such that the function ω(δ)/δ 2 decreases on (0, +g8) while ω is not asymptotically (as δ → 0) equivalent to the second modulus of continuity of any continuous function.
KeywordsContinuous Function Fourier Series STEKLOV Institute Wide Class Closed Interval
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