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  • 1 Loránd Eötvös University Department of Numerical Analysis Budapest Pázmány P. Sétány I/C H-1117 Hungary Budapest Pázmány P. Sétány I/C H-1117 Hungary
  • | 2 Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics Budapest Alfréd Rényi Institute Mathematics Reáltanoda U. 13-15 H--1053 Hungary Reáltanoda U. 13-15 H--1053 Hungary
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Abstract  

Starting from the Lagrange interpolation on the roots of Jacobi polynomials, a wide class of discrete linear processes is constructed using summations. Some special cases are also considered, such as the Fejr, de la Valle Poussin, Cesro, Riesz and Rogosinski summations. The aim of this note is to show that the sequences of this type of polynomials are uniformly convergent on the whole interval [-1,1] in suitable weighted spaces of continuous functions. Order of convergence will also be investigated. Some statements of this paper can be obtained as corollaries of our general results proved in [15].

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