Geodesic
On Quantities of the Type of Modulus of Continuity and Analogs of $K$-Functionals in the Spaces $S^{(p,q)}(\sigma^{m-1})$
Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 251-264

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The paper continues the research of the author begun in 2003–2021. Quantities of the type of modulus of continuity of functions defined on the sphere in the space $S^{(p,q)}(\sigma^{m-1})$ are studied. These quantities are generated by a family of operators of multiplier type. Their equivalence to analogs of $K$-functionals is established.
Keywords: Fourier–Laplace series, $\psi$-derivative, best approximation, modulus of continuity, $K$-functional. 
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     title = {On {Quantities} of the {Type} of {Modulus} of {Continuity} and {Analogs} of $K${-Functionals} in the {Spaces} $S^{(p,q)}(\sigma^{m-1})$},
     journal = {Matemati\v{c}eskie zametki},
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R. A. Lasuriya. On Quantities of the Type of Modulus of Continuity and Analogs of $K$-Functionals in the Spaces $S^{(p,q)}(\sigma^{m-1})$. Matematičeskie zametki, Tome 113 (2023) no. 2, pp. 251-264. http://geodesic.mathdoc.fr/item/MZM_2023_113_2_a7/