λ-Bernstein Operators Based on Pólya Distribution

Abstract

In this manuscript, we propose a Pólya distribution-based generalization of $\lambda$-Bernstein operators. We establish some fundamental results for convergence as well as order of approximation of the proposed operators. We present theoretical result and graph to demonstrate the proposed operator’s intriguing ability to interpolate at the interval’s end points. In order to illustrate the convergence of proposed operators as well as the effect of changing the parameter “$\mu ,$” we provide a variety of results and graphs as our paper’s conclusion.

Keywords:

• $\lambda$-Bernstein operators
• Lipschitz continuous functions
• Pólya-Eggenberger distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• MSC 41A25
• MSC 41A36

Acknowledgments

The authors take this opportunity to express their deep gratitude to the learned referees for several valuable suggestions and constructive comments, which resulted in the subsequent improvement of this research paper.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

This work is supported by the Council of Scientific and Industrial Research (CSIR) with reference no.: 08/133(0029)/2019-EMR-I for the first author.