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    STUDIA MATHEMATICA - Issue no. 4 / 2018  
         
  Article:   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.

Authors:  HARI MOHAN SRIVASTAVA, SHAHID KHAN, QAZI ZAHOOR AHMAD, NAZAR KHAN, SAQIB HUSSAIN.
 
       
         
  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 ∈ C and |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.

Keywords: Analytic functions, univalent functions, Taylor-Maclaurin series rep- resentation, Faber polynomials, bi-inivalent functions, q-derivative operator, q- hypergeometric functions, q-integral operators.
 
         
     
         
         
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