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Modulus of Continuity and Modulus of Smoothness related to the Deformed Hankel Transform

Results in Mathematics, 2021
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Selma Negzaoui, Sara Oukili
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Modulus of Continuity of Piecewise Analytic Functions

Mathematical Notes, 2003
Conditions under which the modulus of continuity \(\omega(f; \delta)\) of a piece-wise real-analytic function \(f : [a, b] \rightarrow {\mathbb R}\) becomes analytic at zero are found. The results obtained are of the following type. Theorem 1. Let \(f\) be piece-wise real-analytic on \([a, b]\). If \[ \sup_{x\in D_{N}} d(x) < \sup_{x\in M\setminus D_{N}
Dovgosheĭ, A. A., Potemkina, L. L.
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A Continuous Modulus of Continuity

The American Mathematical Monthly, 1983
(1983). A Continuous Modulus of Continuity. The American Mathematical Monthly: Vol. 90, No. 2, pp. 126-127.
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Modulus of continuity and Lipschitz approximation

Journal of Mathematical Analysis and Applications, 2018
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Liu, Luofei, Jiang, Yan
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The modulus of continuity in Lp

Mathematical Notes of the Academy of Sciences of the USSR, 1987
Let \(1\leq p\leq \infty\), \(L_ p\) be the space of 1-periodic functions f(x) with the norm \(\| f\|_ p=(\int^{1}_{0}| f(x)| \;pdx)^{1/p}\) \(1\leq ...
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Some properties of the modulus of continuity

Mathematical Notes of the Academy of Sciences of the USSR, 1971
Necessary and sufficient conditions are derived for the continuity and semiadditivity of the modulus of continuity of a functionf(x) given on a compact Ω in n-dimensional euclidean space.
Kolodiĭ, I. M., Hil'debrand, F.
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Modulus of Strong Proximinality and Continuity of Metric Projection

Set-Valued and Variational Analysis, 2010
For a real Banach space \(X\) and a closed subspace \(Y\) of \(X,\) the metric projection is the set-valued mapping \(P_Y:X\rightrightarrows Y\) given by \(P_Y(x)=\{y\in Y : \|x-y\|=d(x,Y)\},\;x\in X\). For \(t>0\) put \(P_Y(x,t)=\{y\in Y : \|x-y\|< d(x,Y)+t\}\).
Dutta, S., Shunmugaraj, P.
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