(p, q)-Sz\'asz-Mirakyan-Baskakov-Stancu type Operators

TL;DR

This paper introduces a Stancu variant of (p, q)-Szász-Mirakyan-Baskakov operators, providing approximation estimates and moment analysis using Steklov mean, extending classical operators with new parameters.

Contribution

It develops a new Stancu variant of (p, q)-Szász-Mirakyan-Baskakov operators and derives approximation properties and moment estimates for this generalized form.

Findings

Derived weighted approximation results.

Established direct estimates via modulus of continuity.

Special case reduces to classical (p, q)-Szász-Mirakyan-Baskakov operators.

Abstract

This deals with the Stancu variant of (p, q)-Sz\'asz-Mirakyan-Baskakov operators. Estimation of moments and establishing few basic approximation results which comprise weighted approximation and direct estimates in view of modulus of continuity is the aim of this paper. Steklov mean method has been used for linear approximation. For the particular case {\alpha} = 0, \b{eta} = 0, we get (p, q) -Sz\'asz-Mirakyan-Baskakov operators.