• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.411-423
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• 2007

This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.293-320
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• 2006

Using calculus inequalities and embedding theorems in $R^1$, we establish $W^1_2$-estimates for the solutions of prey-predator population model with cross-diffusion and self-diffusion terms. Two cases are considered; (i) $d_1\;=\;d_2,\;{\alpha}_{12}\;=\;{\alpha}_{21}\;=\;0$, and (ii) $0\;<\;{\alpha}_{21}\;<\;8_{\alpha}_{11},\;0\;<\;{\alpha}_{12}\;<\;8_{\alpha}_{22}$. It is proved that solutions are bounded uniformly pointwise, and that the uniform bounds remain independent of the growth of the diffusion coefficient in the system. Also, convergence results are obtained when $t\;{\to}\;{\infty}$ via suitable Liapunov functionals.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.395-410
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• 2015

For functions $f(z)=z+a_2z^2+a_3z^3+{\cdots}$ with ${\mid}a_2{\mid}=2b$, $b{\geq}0$, sharp radii of starlikeness of order ${\alpha}(0{\leq}{\alpha}<1)$, convexity of order ${\alpha}(0{\leq}{\alpha}<1)$, parabolic starlikeness and uniform convexity are derived when ${\mid}a_n{\mid}{\leq}M/n^2$ or ${\mid}a_n{\mid}{\leq}Mn^2$ (M>0). Radii constants in other instances are also obtained.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.201-216
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• 2024

The aim of this paper is to study a new and unified class 𝓡^α_Cosh of analytic functions associated with cosine hyperbolic function in the open unit disc E = {z ∈ ℂ : |z| < 1}. Some interesting properties of this class such as initial coefficient bounds, Fekete-Szegö inequality, second Hankel determinant, Zalcman inequality and third Hankel determinant have been established. Furthermore, these results have also been studied for two-fold and three-fold symmetric functions.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.319-330
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• 2020

We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.143-154
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• 2013

We introduce a subclass $S_s^{({\kappa})}$(A,B) (-1 ${\leq}$ B < A ${\leq}$ 1) of functions which are analytic in the open unit disk and close-to-convex with respect to ${\kappa}$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.583-590
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• 2015

This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.

• East Asian mathematical journal
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• v.14 no.1
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• pp.107-116
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• 1998

This paper deals with functions of the form $f(z)=a_1z-{\sum}{\limits}_{n=2}^{\infty}a_nz^n(a_1>0,\;a_n{\geqslant}0)$ with $(1-{\mu})f(z_0)/z_0+{\mu}f'(z_0)=1(-1. We introduce the class $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$ with generalized fractional derivatives. Also we have obtained coefficient inequalities, distortion theorem and radious problem of functions belonging to the calss $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$.

• East Asian mathematical journal
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• v.5 no.1
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• pp.57-67
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• 1989

We introduce a class $L_{\sigma}*({\alpha},{\beta},{\gamma})$ of functions defined by $f*S_{\sigma}(z)$ of f(z) and $S_{\sigma}(z)=z/(1-z)^{2(1-{\sigma})}$. The present paper is to determine extreme point, coefficient inequalities., distortion Theorem and radius of starlikeness and convexity for functions in $L_{\sigma}*({\alpha},{\beta},{\gamma})$. And we give fractional calculus.