Better approximation of function by $\alpha-$Bernstein-P\u{a}lt\u{a}nea operators

TL;DR

This paper introduces a new class of $oldsymbol{ extalpha-}$Bernstein-Pe2lte2nea operators that improve approximation quality, providing convergence rates, error bounds, and asymptotic analysis, supported by computational verification.

Contribution

It proposes a novel modification of $ extalpha-$Bernstein-Pe2lte2nea operators with enhanced approximation properties and establishes theoretical convergence and error estimates.

Findings

Improved approximation order over existing operators

Derived convergence and error estimation results

Validated theoretical findings with MAPLE simulations

Abstract

In this paper, we present a new type of $\alpha-$Bernstein-P\u{a}lt\u{a}nea operators having a better order of approximation than itself. We establish some approximation results concerning the rate of convergence, error estimation and asymptotic formulas for the new modifications. Also, the theoretical results are verified by using MAPLE algorithms.