Unification of the Bernstein-type polynomials and their applications

摘要

In this paper, we investigate some new identities related to the unification of the Bernstein-type polynomials, Bernoulli polynomials, Euler numbers and Stirling numbers of the second kind. We also give some remarks and applications of the Bernstein-type polynomials related to solving high even-order differential equations by using the Bernstein-Galerkin method. We also give some applications on these polynomials and differential equations. MSC:11B68, 12D10, 14F10, 26C05, 26C10, 30B40, 30C15, 42A38, 44A10.