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Certain Subclasses of Bi-Starlike and Bi-Convex Functions of Complex Order

  • MAGESH, NANJUNDAN (Post-Graduate and Research Department of Mathematics, Government Arts College for Men) ;
  • BALAJI, VITTALRAO KUPPARAOo (Department of Mathematics, L. N. Government College)
  • Received : 2014.05.28
  • Accepted : 2015.02.21
  • Published : 2015.09.23

Abstract

In this paper, we introduce and investigate an interesting subclass $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ of analytic and bi-univalent functions of complex order in the open unit disk ${\mathbb{U}}$. For functions belonging to the class $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ we investigate the coefficient estimates on the first two Taylor-Maclaurin coefficients ${\mid}{\alpha}_2{\mid}$ and ${\mid}{\alpha}_3{\mid}$. The results presented in this paper would generalize and improve some recent works of [1],[5],[9].

Keywords

Univalent;Bi-Univalent functions;Starlike and Convex functions Ma-Minda type;Bi-Starlike of Ma-Minda type;Bi-Convex of Ma-Minda type

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