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1. -functionals and multivariate Bernstein polynomials

Author

Ding, Chunmei and Cao, Feilong

Subjects
*BERNSTEIN polynomials, *APPROXIMATION theory, *MATHEMATICAL inequalities, *BOOLEAN algebra, *MATHEMATICAL analysis, *STOCHASTIC convergence
Abstract

Abstract: This paper estimates upper and lower bounds for the approximation rates of iterated Boolean sums of multivariate Bernstein polynomials. Both direct and inverse inequalities for the approximation rate are established in terms of a certain -functional. From these estimates, one can also determine the class of functions yielding optimal approximations to the iterated Boolean sums. [Copyright &y& Elsevier]

Published
2008
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2. Approximation theorems for localized szsz–Mirakjan operators

Author

Xie, Linsen and Xie, Tingfan

Subjects
*APPROXIMATION theory, *INTEGRAL theorems, *STOCHASTIC convergence, *MATHEMATICAL analysis
Abstract

Abstract: In the present paper, we investigate the convergence and the approximation order of the localized Szsz–Mirakjan operators, and obtain some new results to improve the results due to Omey [Note on operators of Szsz–Mirakjan type, J. Approx. Theory 47 (1986) 246–254]. [Copyright &y& Elsevier]

Published
2008
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