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511.4 ANAS

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 Description
 viii, 150 pages ; 24 cm
 Notes
 1. Quantitative approximation by complex BernsteinSchurer and KantorovichSchurer polynomials on compact disks  2. Quantitative approximation by complex BernsteinDurrmeyer polynomials on compact disks  3. Quantitative overconvergence for Chebyshev and Legendre orthogonal expansions on compact interval  4. Quantitative overconvergence for singular integrals on a strip  5. Quantitative overconvergence for generalized singular integrals on a strip  6. Approximation properties of multicomplex singular integrals in the unit polydisk  7. Quantitative estimates in the overconvergence of multivariate singular integrals on a polystrip 91  8. Approximation properties of multivariate generalized singular integrals in the unit polydisk  9. Quantitative estimates in the overconvergence of complex multivariate generalized singular integrals in polystrips  10. Best approximation of vector valued functions by generalized polynomials.In this monograph we study quantitatively the order of simultaneous approximation and Voronovskaja type asymptotic results for complex BernsteinSchurer, KantorovichSchurer and BernsteinDurrmeyer polynomials related to analytic functions on compact disks. In this way the overconvergence phenomenon for BernsteinSchurer and BernsteinDurrmeyer polynomials is revealed. We continue with explicit quantitative estimates for the overconvergence in the complex plane of the partial sums of the Fouriertype expansions on [1, 1] with respect to Chebyshev and Legendre orthogonal polynomials. Furthermore we obtain quantitative estimates in the overconvergence phenomenon for the classical and generalized singular integrals of GaussWeierstrass, PoissonCauchy and Picard on a strip. Furthermore we present Jackson type approximation results by generalizations of multicomplex Picard, PoissonCauchy and GaussWeierstrass singular integrals in terms of higher order moduli of smoothness on polydisks. It follows quantitative estimates in the overconvergence phenomenon on polystrips, for the weighted and nonweighted cases, for generalized multicomplex singular integrals of Picard, PoissonCauchy and GaussWeierstrass types. We establish basic results concerning the best approximation of vectorvalued functions by generalized polynomials. The overconvergence of singular integrals is presented for the first time in book form. This monograph is intended for researchers, graduate students working in many areas of pure and applied mathematics  P. 4 of cover.Includes bibliographical references and index.