• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.37-47
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• 2010

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 $D^m_{{\lambda},{\mu}}$.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.307-318
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• 2018

In this paper, we obtain $Fekete-Szeg{\ddot{o}}$ inequalities for certain class of meromorphic functions f(z) for which $-{\frac{(1-{\frac{{\alpha}}{q}})qzD_qf(z)+{\alpha}qzD_q[zD_qf(z)]}{(1-{\frac{{\alpha}}{q}})f(z)+{\alpha}zD_qf(z)}{\prec}{\varphi}(z)$(${\alpha}{\in}{\mathbb{C}}{\backslash}(0,1]$, 0 < q < 1). Sharp bounds for the $Fekete-Szeg{\ddot{o}}$ functional ${\mid}{\alpha}_1-{\mu}{\alpha}^2_0{\mid}$ are obtained.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.591-601
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• 2017

In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.679-688
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• 2015

In this paper, we obtain Fekete-$Szeg{\ddot{o}}$ inequalities for certain subclasses of analytic univalent functions of complex order associated with quasi-subordination.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.13-23
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• 2013

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.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.611-619
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• 2018

In this paper, we obtain initial coefficient bounds for an unified subclass of analytic functions by using the Chebyshev polynomials. Furthermore, we find the Fekete-$Szeg{\ddot{o}}$ result for this class. All results are sharp. Consequences of the results are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1937-1943
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• 2015

For $1{\leq}{\alpha}<2$, let $\mathcal{F}({\alpha})$ denote the class of locally univalent normalized analytic functions $f(z)=z+{\Sigma}_{n=2}^{\infty}{a_nz^n}$ in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\left|z\right|}<1\}$ satisfying the condition $Re\(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\)>{\frac{{\alpha}}{2}}-1$. In the present paper, we shall obtain the sharp upper bound for Fekete-$Szeg{\ddot{o}}$ functional $|a_3-{\lambda}a_2^2|$ for the complex parameter ${\lambda}$.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.953-967
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• 2015

In this article, by making use of a linear multiplier fractional differential operator $D^{{\delta},m}_{\lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-$Szeg{\ddot{o}}$ inequalities.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.357-367
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• 2001

Let $Q(\beta)$ be the class of normalized strongly quasiconvex functions of order $\beta$ in the open unit disk. Sharp Fekete-Szego inequalities are obtained for functions belonging to the class $Q(\beta)$. We also consider the integral preserving properties in a sector.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.443-452
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• 2014

In the present investigation we consider Fekete-Szeg$\ddot{o}$ problem with complex parameter ${\mu}$ and also find upper bound of the second Hankel determinant ${\mid}a_2a_4-a^2_3{\mid}$ for functions belonging to a new class $S^{\tau}_{\gamma}(A,B)$ using Toeplitz determinants.