The Faber polynomial expansion method and its application to the general coefficient problem for some subclasses of bi-univalent functions associated with a certain q-integral operator
DOI:
https://doi.org/10.24193/subbmath.2018.4.01Keywords:
Analytic functions, univalent functions, Taylor-Maclaurin series representation, Faber polynomials, bi-inivalent functions, q-derivative operator, q- hypergeometric functions, q-integral operators.Abstract
In our present investigation, we first introduce several new subclasses of analytic and bi-univalent functions by using a certain q-integral operator in the open unit disk U = {z : z ∈ Cand |z| < 1}. By applying the Faber polynomial expansion method as well as the q-analysis, we then determine bounds for the nth coefficient in the Taylor-Maclaurin series expansion for functions in each of these newly-defined analytic and bi-univalent function classes subject to a gap series condition. We also highlight some known consequences of our main results.
Mathematics Subject Classification (2010): 05A30, 30C45, 11B65, 47B38.
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