• 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.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.503-511
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• 2021

In this present work, we obtain certain coefficients of the subclass 𝓗_λ,𝛄(s, b, n) of non-Bazilević functions and estimate the relevant connection to the famous classical Fekete-Szegö inequality of functions belonging to this class.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.589-598
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• 2006

In the present investigation, sharp upper bounds of $|a3-{\mu}a^2_2|$ for functions $f(z)=z+a_2z^2+a_3z^3+...$ belonging to certain subclasses of starlike and convex functions with respect to symmetric points are obtained. Also certain applications of the main results for subclasses of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szego inequalities for certain classes of functions defined through fractional derivatives are obtained.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.307-319
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• 2022

The present paper deals with the upper bound of third order Hankel determinant for a certain subclass of analytic functions associated with Cardioid domain in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results proved here generalize the results of several earlier works.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.513-522
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• 2021

In this paper we investigate a subclass 𝓜(α) of the class of starlike functions in the unit disk |z| < 1. 𝓜(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition $$1+\frac{{\alpha}-{\pi}}{2\;sin\;{\alpha}}. The class 𝓜(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639-1649, 2017]. In this paper some basic geometric properties of the class 𝓜(α) are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szegö functional associated with the k-th root transform [f(z^k)]^1/k. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained.