Blending type approximation by τ-Baskakov-Durrmeyer type hybrid operators

Abstract

Abstract In this work, we construct a Durrmeyer type modification of the τ -Baskakov operators depends on two parameters $\alpha &gt;0$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> and $\tau \in [0,1]$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:math> . We derive the rate of approximation of these operators in a weighted space and also obtain a quantitative Voronovskaja type asymptotic formula as well as a Grüss Voronovskaya type approximation.

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