Some properties of a new kind of modulus of smoothness
Copyright policy )Some properties of a new kind of modulus of smoothness
The modulus of smoothness \omega (f, \delta)_{\varphi, p} = \mathrm {sup}_{0 < h ≤ \delta} \| \Delta^2_{h, \varphi} \|_{L^p} has arisen during the investigation of positive operators of the Kantorovich type. Here we show that \omega_{\varphi, p} resembles the ordinary case \varphi = 1 and we give the characterization of those functions f for which \omega (f, \delta)_{\varphi, p} = O (\delta^2) . The results obtained have applications to positive operators.
- University of Szeged Hungary
Best approximation, Chebyshev systems, best polynomial approximation, Approximation by polynomials, modulus of smoothness, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, Functions of bounded variation, generalizations, Approximation by positive operators, Rate of convergence, degree of approximation, contractive operation processes, Interpolation in approximation theory, optimal order
Best approximation, Chebyshev systems, best polynomial approximation, Approximation by polynomials, modulus of smoothness, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, Functions of bounded variation, generalizations, Approximation by positive operators, Rate of convergence, degree of approximation, contractive operation processes, Interpolation in approximation theory, optimal order
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!