• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.481-491
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• 2019

In the present paper, we investigate the upper bounds on third order Hankel determinants for certain class of close-to-convex functions in the unit disk. Furthermore, we obtain estimates of the Zalcman coefficient functional for this class.

• 대한수학회보
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• 제60권5호
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• pp.1253-1263
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• 2023

Let 𝓤⁺ be the class of analytic functions f such that ${\frac{z}{f(z)}}$ has real and positive coefficients and f^-1 be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for f, as well as, sharp estimates of the second and the third Hankel determinant for f and f^-1. We also show that the Zalcman conjecture holds for functions f from 𝓤⁺.

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.387-399
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• 2020

In this paper, we study a problem of a non-constant entire function f that shares a set S = {a, b, c} with its k-th derivative f^(k), where a, b and c are any three distinct complex numbers. We have found a gap in the statement of the main result of Chang-Fang-Zalcman [10], and with the help of their method, we have generalize their result in a more compact form. As an application, we generalize the famous Brück conjecture [9] with the idea of set sharing.