The family of $ \lambda $-Bernstein-Durrmeyer operators based on certain parameters

Ram Pratap

doi:10.3934/mfc.2022038

Article Contents

2023, Volume 6, Issue 3: 546-557. Doi: 10.3934/mfc.2022038

This issue Previous Article Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators Next Article Fuzzy approximation based on $ \tau- \mathfrak{K} $ fuzzy open (closed) sets

The family of $ \lambda $-Bernstein-Durrmeyer operators based on certain parameters

Ram Pratap

Department of Mathematics, Hansraj College, University of Delhi, 110007, India

Dedicate to Professor Vijay Gupta, Netaji Subhas University of Technology, India on his 60-th birthday

Received: June 2022

Revised: September 2022

Early access: September 29, 2022

Published online: September 29, 2022

This work was carried out at Miranda House, University of Delhi, India-110007.

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Abstract

The primary goal of this paper is to present the generalization of $ \lambda $-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.

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Mathematics Subject Classification: Primary: 41A36; Secondary: 41A25.

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