Coefficients bounds for a subclass of q-bi-starlike functions associated with the generalized q-Lommel polynomials

Abstract

Orthogonal q-polynomials, both new and old, have witnessed a huge and revived attention in recent years, because of their applications in many diverse areas of mathematics and other sciences. In Geometric Function Theory, different subclasses of analytic and bi-univalent functions have been investigated and studied involving different orthogonal q-polynomials. In our present investigation, motivated by these recent research going on, first, we define some new subclasses of q-bi-starlike functions with the help of certain q-derivative operator which involving the generalized q-Lommel polynomials and q-Chebyshev polynomials. We then obtain the initial coefficients bounds for our defined function classes. Furthermore, the Fekete–Szegö inequalities are obtained for these defined function classes.

Keywords

• Analytic and bi-univalent functions
• starlike and q-starlike functions
• subordination
• q-derivative operator
• q-Lommel polynomials
• q-Chebyshev polynomials