• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1035-1041
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• 2022

Herein, we construct a qualitative subclass B^γ(κ, µ, σ) of the class of analytic bi-univalent functions. Next, we explore estimates of the coefficients |a_j| (j = 1, 2) and the Fekete-Szegö functional |a₃ - ςa²₂| for functions in this subclass.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.477-484
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• 2020

For a non-zero complex number b and for m and n in 𝒩₀ = {0, 1, 2, …} let Ψ_n,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dⁿ f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a₃ - 𝜇a²₂| are obtained.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.521-534
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• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• 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.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.715-727
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• 2021

In this paper, we give some results an upper bound of Hankel determinant of H₂(1) for the classes of 𝓝 (𝜶). We get a sharp upper bound for H₂(1) = c₃ - c²₂ for 𝓝 (𝜶) by adding z₁, z₂, …, z_n zeros of f(z) which are different than zero. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained. Finally, the sharpness of the inequalities obtained in the presented theorems are proved.