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Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

Orhan, Halit;Yagmur, Nihat;Caglar, Murat

  • 투고 : 2011.03.16
  • 심사 : 2012.07.24
  • 발행 : 2013.03.23

초록

In this present work, the authors obtain Fekete-Szeg$\ddot{o}$ inequality for certain normalized analytic function $f(z)$ defined on the open unit disk for which $$\frac{{\lambda}{\beta}z^3(L(a,c)f(z))^{{\prime}{\prime}{\prime}}+(2{\lambda}{\beta}+{\lambda}-{\beta})z^2(L(a,c)f(z))^{{\prime}{\prime}}+z(L(a,c)f(z))^{{\prime}}}{{\lambda}{\beta}z^2(L(a,c)f(z))^{{\prime}{\prime}}+({\lambda}-{\beta})z(L(a,c)f(z))^{\prime}+(1-{\lambda}+{\beta})(L(a,c)f(z))}\;(0{\leq}{\beta}{\leq}{\lambda}{\leq}1)$$ lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szeg$\ddot{o}$ inequality for a class of functions defined through fractional derivatives are obtained.

키워드

Fekete-Szeg$\ddot{o}$ problem;Analytic function;Coefficient inequality

참고문헌

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피인용 문헌

  1. Coefficient Bounds for Certain Analytic Functions 2016, https://doi.org/10.5666/KMJ.2013.53.1.13