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Approximation properties of certain summation integral type operators

Patel P., Mishra V. N.

Demonstratio Mathematica

2015

Vol. 48, nr 1

77--90

In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

On the strong approximation of functions by the Bernstein polynomials

Michałowicz A.

Fasciculi Mathematici

2007

Nr 37

27-33

In this note we introduce the strong differences of function and its Bernstein polynomials and give approximation theorems for them. This note is motivated by results on the strong summability of trigonometric Fourier series given in [2] and by the paper [5].