Some general statistical approximation results for $ \lambda $-Bernstein operators

TL;DR

This paper establishes new statistical approximation results for λ-Bernstein operators, including a Voronovskaja-type theorem and the construction of bivariate operators, enhancing understanding of their approximation capabilities.

Contribution

It introduces general statistical approximation results for λ-Bernstein operators and develops bivariate versions, expanding their theoretical framework.

Findings

Proved a statistical Voronovskaja-type approximation theorem.

Constructed and analyzed bivariate λ-Bernstein operators.

Demonstrated improved approximation properties of these operators.

Abstract

In this article, we achieve some general statistical approximation results for $ \lambda $-Bernstein operators in addition to some other approximation properties. We prove a statistical Voronovskaja-type approximation theorem. We also construct bivariate $\lambda $-Bernstein operators and study their approximation properties.