A new approach to modified q-Bernstein polynomials for functions of two variables with their generating and interpolation functions

TL;DR

This paper introduces a novel approach to modified q-Bernstein polynomials for two-variable functions, deriving recurrence relations, identities, generating functions, and interpolation functions to enhance their mathematical understanding.

Contribution

It presents new formulations, identities, and generating functions for modified q-Bernstein polynomials of two variables, expanding their theoretical framework.

Findings

Derived recurrence formulas and identities involving Stirling numbers and Bernoulli polynomials.

Established generating and interpolation functions for the modified q-Bernstein polynomials.

Calculated derivatives of these polynomials and their generating functions.

Abstract

The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second kind Stirling numbers and generalized Bernoulli polynomials. Moreover, we give the generating function and interpolation function of these modified q-Bernstein polynomials of two variables and also give the derivatives of these polynomials and their generating function.