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Convergence of α-Bernstein-Durrmeyer operators about a collection of measures

  • Harmanjit Kaur and Meenu Rani Goyal EMAIL logo
Published/Copyright: February 25, 2025
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Abstract

This work offers a generalization of the α-Bernstein-Durrmeyer operators Dm,Zα about a collection Z of arbitrary measures, with the goal of building a bridge between approximation, probability, and measure theory. It has been discussed how to achieve pointwise convergence of Dm,Zα and constraints on measure collection have been developed for these operators’ convergence. With certain values of the measures considered, the generalization yields a range of Bernstein-like operators with their α variation. In order to handle a wider variety of p.l.o. and investigate their convergence, the paper comprises numerous operators, making it a useful tool.

Funding statement: This work is supported by National Board of Higher Mathematics – Department of Atomic Energy (NBHM-DAE), Government of India (Sanction No. 02011/25/2021/NBHM(RP)/R&D II/7997) and Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, India. We are also thankful to Ministry of Science & Technology, Department of Science & Technology, Government of India, for providing the optimal infrastructure facilities under FIST project.

  1. (Communicated by David Buhagiar)

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Received: 2024-05-29
Accepted: 2024-08-23
Published Online: 2025-02-25
Published in Print: 2025-02-25

© 2025 Mathematical Institute Slovak Academy of Sciences

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