Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution

Document Type : Original Article

Authors

Lakshmi Narayan Mishra ¹

Alok Kumar ²

¹ Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.

² Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar- 249411, Uttarakhand, India.

10.22034/kjm.2019.85886

Abstract

In this paper, we study approximation properties of a family of linear positive operators and establish the Voronovskaja type asymptotic formula, local approximation and pointwise estimates using the Lipschitz type maximal function. In the last section, we consider the King type modification of these operators to obtain better estimates.

Keywords

Asymptotic formula

modulus of continuity

$K$-functional

Polya distribution

local approximation

Subjects

• 26 Real functions
• 40 Sequences, series, summability
• 41 Approximations and expansions

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