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A generalized trapezoid inequality for functions of bounded variation
2000Let \(f\) be a real function of bounded variation on \([a,b]\) . Denote its total variation on that interval by \(\bigvee_{a}^{b}\left( f\right) \) . The authors prove the following inequality \[ \left|\int_{a}^{b}f(t)dt-f(a)(x-a)-f(b)(b-x)\right|\leq \left[ \frac{1}{2} (b-a)+\left|x-\frac{a+b}{2}\right|\right] \bigvee_{a}^{b}\left( f\right) \] for all
Cerone, P. +2 more
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Journal of Applied Analysis, 2000
The author presents several properties of function spaces of bounded generalized variation of Riesz-Orlicz type including weight and then proves that each globally Lipschitzian superposition (or Nemytskij) operators between two such spaces must be affine.
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The author presents several properties of function spaces of bounded generalized variation of Riesz-Orlicz type including weight and then proves that each globally Lipschitzian superposition (or Nemytskij) operators between two such spaces must be affine.
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Sbornik: Mathematics, 2002
This paper is an investigation of necessary and sufficient conditions for embeddings of the function classes in classes of functions of bounded generalized variation. Theorems of a general character are obtained, along with embedding theorems under certain additional conditions imposed on the modulus of continuity.
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This paper is an investigation of necessary and sufficient conditions for embeddings of the function classes in classes of functions of bounded generalized variation. Theorems of a general character are obtained, along with embedding theorems under certain additional conditions imposed on the modulus of continuity.
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The expanding regulatory mechanisms and cellular functions of circular RNAs
Nature Reviews Molecular Cell Biology, 2020Ling-Ling Chen
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Gene regulation by long non-coding RNAs and its biological functions
Nature Reviews Molecular Cell Biology, 2020Luisa Statello +2 more
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A framework for understanding the functions of biomolecular condensates across scales
Nature Reviews Molecular Cell Biology, 2020Michael K Rosen
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Global view of human protein glycosylation pathways and functions
Nature Reviews Molecular Cell Biology, 2020Katrine T Schjoldager +2 more
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Long non-coding RNAs: definitions, functions, challenges and recommendations
Nature Reviews Molecular Cell Biology, 2023John S Mattick +2 more
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Lagrange interpolation of functions of generalized bounded variation
Acta Mathematica Hungarica, 1989openaire +1 more source
BANACH ALGEBRAS OF FUNCTIONS HAVING GENERALIZED BOUNDED VARIATION
Real Analysis Exchange, 1986openaire +1 more source