Geodesic
Equivalence Between K-functionals Based on Continuous Linear Transforms
Serdica Mathematical Journal, Tome 33 (2007) no. 4, pp. 475-494.

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The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.
Keywords: K-Functional, Modulus of Smoothness, Rate of Convergence, Best Approximation, Linear Operator 
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     author = {Draganov, Borislav and Ivanov, Kamen},
     title = {Equivalence {Between} {K-functionals} {Based} on {Continuous} {Linear} {Transforms}},
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Draganov, Borislav; Ivanov, Kamen. Equivalence Between K-functionals Based on Continuous Linear Transforms. Serdica Mathematical Journal, Tome 33 (2007) no. 4, pp. 475-494. http://geodesic.mathdoc.fr/item/SMJ2_2007_33_4_a5/