Abstract
In this paper, we investigate approximation properties of the Stancu type generalization of the $\alpha$-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Gruss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.
Highlights
It is very well known that the polynomial approximation of continuous functions has an important role in numerical analysis
N xk (1 − x)n−k, k inspired by the binomial probability distribution
We provide the uniform convergence property and we estimate the rate of convergence by using moduli of continuity
Summary
It is very well known that the polynomial approximation of continuous functions has an important role in numerical analysis. The main purpose is to study some important results concerning uniform convergence and estimates of the new linear positive operators, which are direct applications of the properties and formulas recalled in the first section.
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