• Honam Mathematical Journal
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• v.23 no.1
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• pp.41-50
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• 2001

This paper concerns with the subclass of normalized analytic function f in D = {z : |z| < 1}, namely a ${\delta}$-convex function in a sector. This subclass is denoted by ${\Delta}({\delta})$, where ${\delta}$ is a real positive. Given $0<{\beta}{\leq}1$ then for $z{\in}D$, the exact ${\alpha}({\beta},\;{\delta})$ is found such that $f{\in}{\Delta}({\delta})$ implies $f{\in}S^*({\beta})$, where $S^*({\beta})$ is starlike of order ${\beta}$ in a sector. This work is a more general version of the result of Nunokawa and Thomas [11].

• Honam Mathematical Journal
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• v.37 no.4
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• pp.513-527
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• 2015

In this paper, we first introduce and study new concepts of ($k_1,{\cdots},k_n$)-convexity and k-segment. Secondly, we shall discuss some properties of nonisotropically starlike domains in $\mathbb{R}^n$ with respect to the origin.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.215-224
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• 2019

In the present paper, some generalizations of analytic functions have been considered and the bounds of the coefficients of these classes of bi-univalent functions have been investigated.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.81-93
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• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.429-438
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• 2015

The objective of this paper is to obtain sharp upper bound for the second Hankel functional associated with the $k^{th}$ root transform $[f(z^k)]^{\frac{1}{k}}$ of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.455-472
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• 2022

For j = 0, 1, 2,…, k - 1; k ≥ 2; and - 1 ≤ B < A ≤ 1, we have introduced the functions classes denoted by ST_[j,k](A, B) and K_[j,k](A, B), respectively, called the generalized (j, k)-symmetric starlike and convex functions. We first proved the sharp bounds on |f(z)| and |f'(z)|. Various radii related problems, such as radius of (j, k)-symmetric starlikeness, convexity, strongly starlikeness and parabolic starlikeness are determined. The quantity |a²₃ - a₅|, which provide the initial bound on Zalcman functional is obtained for the functions in the family ST_[j,k]. Furthermore, the sharp pre-Schwarzian norm is also established for the case when f is a member of K_[j,k](α) for all 0 ≤ α < 1.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1025-1039
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• 2022

For given non-negative real numbers 𝛼_k with ∑^m_k=1 𝛼_k = 1 and normalized analytic functions f_k, k = 1, …, m, defined on the open unit disc, let the functions F and Fn be defined by F(z) := ∑^m_k=1 𝛼_kf_k(z), and F_n(z) := n^-1 ∑^n-1_j=0 e^-2j𝜋i/nF(e^2j𝜋i/nz). This paper studies the functions f_k satisfying the subordination zf'_k(z)/F_n(z) ≺ h(z), where the function h is a convex univalent function with positive real part. We also consider the analogues of the classes of starlike functions with respect to symmetric, conjugate, and symmetric conjugate points. Inclusion and convolution results are proved for these and related classes. Our classes generalize several well-known classes and the connections with the previous works are indicated.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.597-610
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• 2016

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, $G({\lambda},{\alpha})$ and $M({\lambda},{\alpha})$. Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.659-668
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• 2000

Let's $S_n(p,\alpha)(p,n\in\ N={1,2,3,\cdots},0\leq\ \alpha<1)$ denote tje c;ass pf fimctopms $f(z)=z^p+a_{p+z}z^{p+n}+\cdots$ which are $\rho$-valently starlike of order $\alpha$ in the unit disk.Some criteria for a function f(z) to be in the class $S_n(\rho,\alpha)$ are given.