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\title[Coefficient inequalities]
{\large Coefficient inequalities for certain classes of analytic functions using $q$-derivatives}


\author[S. Varadharajan]{S.VARADHARAJAN}




\author[C. Selvaraj]{C. SELVARAJ}



\author[K. R. Karthikeyan]{K. R. KARTHIKEYAN}



\begin{abstract}

We introduce and we study the classes $\mathcal{ST}_{q} \left(g, \lambda, \gamma, \alpha,\beta \right)$ and \linebreak $\mathcal{KV}_{q} \left(g, \lambda, \gamma, \alpha,\beta \right)$ of analytic functions which are defined by making use of the $q$-derivative operator. Coefficient inequalities for functions in these classes are discussed. Some interesting consequences of the results are also pointed out.

\end{abstract}



\begin{amssubject}

30C45; 30C50.

\end{amssubject}



\begin{keyword}

Analytic function, univalent function, starlike function, convex function, convolution, $q$-derivative operator.

\end{keyword}



\thanks{The authors thank the referee for his helpful comments and suggestions.}



\maketitle

\let\thefootnote\relax\footnote{ \ }\hspace{-5mm}\let\thefootnote\relax\footnote{\hspace{-13pt}DOI: 10.24193/mathcluj.2020.2.08}



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\vspace{10pt}



\hspace{-4mm}{\small{Received April 11, 2019}}\\
\hspace{-4mm}{\small{Accepted October 16, 2019}}



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\ \hfill 
\begin{tabular}{c}
{\small\em Al Musanna College of Technology}\\
{\small\em Department of Information Technology}\\
{\small\em Mathematics Section}\\
{\small\em Muscat, Sultanate of Oman}\\ 
{\small\em E-mail: {\tt svrajanram@gmail.com}} \\ \\
{\small\em Presidency College (Autonoumous)}\\
{\small\em Department of Mathematics}\\
{\small\em Chennai, Tamilnadu, India}\\
{\small\em E-mail: {\tt pamc9439@yahoo.co.in}} \\ \\
{\small\em National University of Science and Technology}\\
{\small\em Department of Applied Mathematics and Science}\\
{\small\em Muscat, Sultanate of Oman}\\
{\small\em E-mail: {\tt kr\_karthikeyan1979@yahoo.com}} \\
\end{tabular}



\end{document}
