• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.169-182
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• 2011

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.85-101
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• 1999

Let $p$ be analytic in the unit disc U and let $q$ be univalent in U. In addition, let ${\Omega}$ be a set in C and let ${\psi}:c^3{\times}U{\rightarrow}C$. The author determines conditions on ${\psi}$ so that $$\{{\psi}(p(z),zp^{\prime}(z),z^2p^{{\prime}{\prime}}(z);z){\mid}z{\in}U\}{\subset}{\Omega}{\Rightarrow}p(U){\subset}q(U)$$. Applications of this result to differential inequalities, differential subordinations and integral inequalities are presented.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.647-665
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• 2004

The existence of solutions for the nonlinear functional differential equation with nonlocal conditions governed by the variational inequality is studied. The regularity and a variation of solutions of the equation are also given.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.563-569
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• 2005

In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.147-156
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• 2007

We introduce the extremal length and examine its properties. And we consider the geometric applications of extremal length to the boundary behavior of analytic functions, conformal mappings. We derive the theorem in connection with the capacity. This theorem applies the extremal length to the analytic function defined on the domain with a number of holes. And we obtain the theorems in connection with the pure geometric problems.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1035-1046
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• 2015

In this work we present some geometric properties (like star-likeness and convexity of order ${\alpha}$ and also close-to-convexity of order ($1+{\alpha}$)/2) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{{\mu},{\upsilon}}(z)$ to belong to the Hardy space $H^p$.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.733-748
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• 2018

In this paper, we investigate a new subclass $S^{{\varphi},{\lambda}}_{{\Sigma}_m}$ of ${\Sigma}_m$ consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-$Szeg{\ddot{o}}$ inequalities for this class. Also, we establish estimates for the coefficients for this subclass and several related classes are also considered and connections to earlier known results are made.

• 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.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.163-178
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• 2023

We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function p defined on the unit disc so that the function p is subordinate to the function e^z. These results are applied to find sufficient conditions for the normalised analytic functions f defined on the unit disc to satisfy the subordination zf'(z)/f(z) ≺ e^z.