Incomplete q-Chebyshev Polynomials

In this paper, we get the generating functions of the q-Chebyshev polynomials using eta(z) operator, which is eta(z) f(z)) = f(qz) for any given function f (z). Also considering explicit formulas of the q-Chebyshev polynomials, we give new generalizations of the q-Chebyshev polynomials called the incomplete q-Chebyshev polynomials of the first and second kind. We obtain recurrence relations and several properties of these polynomials. We show that there are connections between the incomplete q-Chebyshev polynomials and the some well-known polynomials