Abstract
In this paper, an extension of the idea of the best approximation in the Hölder spaces with respect to Fourier-Jacobi operators by moduli of smoothness is studied. A special form of the moduli of smoothness is considered to get a strong convergence. Further, advanced approaches of approximation and some direct and inverse results are proved. Moreover, the Jackson-type estimate of functions in Hölder spaces by Jacobi transformations to algebraic polynomials with generalized de la Vallée Poussin mean are established.
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