Geodesic
On Vall\'ee-Poissin means for special series with respect to ultraspherical Jacobi polynomials with sticking partial sums
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2018), pp. 68-80

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This paper continues studying of special series with sticking property ($r$-fold coincidence at points $\pm1$) in ultraspherical Jacobi polynomials, that was started in the works of the first author. Investigation of current paper is paid on approximative properties of Vallée-Poussin means for partial sums of mentioned special series with sticking property. It is shown that for function $f$ with certain smoothness properties at the ends of interval $[-1,1]$ the weighted approximation rate by Vallée-Poussin means has the same order as the best weighted approximation of $f$.
Keywords: Jacobi polynomials, special (sticking) series of ultraspherical polynomials, approximation properties, weighted approximation, Vallée-Poussin means. 
@article{IVM_2018_9_a6,
     author = {I. I. Sharapudinov and M. G. Magomed-Kasumov},
     title = {On {Vall\'ee-Poissin} means for special series with respect to ultraspherical {Jacobi} polynomials with sticking partial sums},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {68--80},
     publisher = {mathdoc},
     number = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_9_a6/}
}
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I. I. Sharapudinov; M. G. Magomed-Kasumov. On Vall\'ee-Poissin means for special series with respect to ultraspherical Jacobi polynomials with sticking partial sums. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2018), pp. 68-80. http://geodesic.mathdoc.fr/item/IVM_2018_9_a6/