A study on the q-Euler numbers and the fermionic q-integrals of the product of several type $q$-Bernstein polynomials on Zp

TL;DR

This paper explores properties of q-Bernstein polynomials connected to q-Euler numbers using fermionic q-integrals on Zp, contributing to the understanding of q-analogues in p-adic analysis.

Contribution

It introduces new properties of q-Bernstein polynomials related to q-Euler numbers via fermionic q-integrals on Zp.

Findings

Derived relationships between q-Bernstein polynomials and q-Euler numbers.

Established properties of fermionic q-integrals on Zp.

Enhanced understanding of q-analogues in p-adic analysis.

Abstract

In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.