The Faber polynomial expansion method and the Taylor-Maclaurin coefficient estimates of Bi-Close-to-Convex functions connected with the <em>q</em>-convolution

Abstract

In this paper, we introduce a new class of analytic and bi-close-to-convex functions connected with q-convolution, which are defined in the open unit disk. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this subclass by using the Faber polynomial expansion method. Several corollaries and consequences of our main results are also briefly indicated.

Keywords

• analytic functions
• univalent functions
• bieberbach conjecture (de branges theorem)
• carathéodory lemma
• faber polynomial expansion
• bi-close-to-convex functions
• convolution of analytic functions
• <i>q</i>-derivative (or <i>q</i>-difference) operator
• <i>q</i>-convolution
• poisson operator and pascal distribution operator