Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

  • Orhan, Halit (Department of Mathematics, Faculty of Science, Ataturk University) ;
  • Yagmur, Nihat (Department of Mathematics, Faculty of Science and Art, Erzincan University) ;
  • Caglar, Murat (Department of Mathematics, Faculty of Science, Ataturk University)
  • Received : 2011.03.16
  • Accepted : 2012.07.24
  • Published : 2013.03.23
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Abstract

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.

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References

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