Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter δ_0

Ali Jassim Mohammad, Hadeel Omar Muslim

Abstract

In this paper, we define a new sequence of linear positive operators of integral type to approximate functions in the space,. First, we study the basic convergence theorem in simultaneous approximation and then study Voronovskaja-type asymptotic formula. Then, we estimate an error occurs by this approximation in the terms of the modulus of continuity. Next, we give numerical examples to approximate three test functions in the space by the sequence. Finally, we compare the results with the classical sequence of Szãsz operators  on the interval . It turns out that, the sequence  gives better than the results of the sequence  for the two test functions using in the numerical examples.

Keywords

Weierstrass approximation theorem; linear positive operators; Simultaneous approximation; Voronovaskaja-type asymptotic formula; Modulus of continuity.

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