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The Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions

  • Deniz, Erhan (Department of Mathematics, Faculty of Science, Ataturk University) ;
  • Orhan, Halit (Department of Mathematics, Faculty of Science, Ataturk University)
  • 투고 : 2008.11.05
  • 심사 : 2009.10.21
  • 발행 : 2010.03.31

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 $\frac{(1-{\alpha})z(D^m_{{\lambda},{\mu}}f(z))'+{\alpha}z(D^{m+1}_{{\lambda},{\mu}}f(z))'}{(1-{\alpha})D^m_{{\lambda},{\mu}}f(z)+{\alpha}D^{m+1}_{{\lambda},{\mu}}f(z)}$ ${\alpha}{\geq}0$) 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 is obtained. The motivation of this paper is to generalize the Fekete-Szeg$\ddot{o}$ inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator $D^m_{{\lambda},{\mu}}$.

키워드

참고문헌

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  3. Coefficient Estimates and Other Properties for a Class of Spirallike Functions Associated with a Differential Operator vol.2013, 2013, https://doi.org/10.1155/2013/415319
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  5. Classes of Analytic Functions Defined by a Differential Operator Related to Conic Domains vol.67, pp.9, 2016, https://doi.org/10.1007/s11253-016-1159-8
  6. Certain Subclasses of Multivalent Functions Defined by New Multiplier Transformations vol.36, pp.6, 2011, https://doi.org/10.1007/s13369-011-0103-3
  7. Fekete-Szegö Problem for a Generalized Subclass of Analytic Functions vol.53, pp.1, 2013, https://doi.org/10.5666/KMJ.2013.53.1.13
  8. On coefficient bounds of some new subfamilies of close-to-convex functions of complex order related to generalized differential operator pp.1793-7183, 2018, https://doi.org/10.1142/S1793557120500497