• International Journal of Fuzzy Logic and Intelligent Systems
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• 제16권2호
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• pp.140-146
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• 2016

This paper proposes a control method of the Segway with unknown control coefficient and input saturation. To design a simple controller for the Segway with the model uncertainty, the prescribed performance function is used. Furthermore, an auxiliary variable is introduced to deal with unknown time-varying control coefficient and input saturation problem. Due to the auxiliary variable, function approximators are not used in this paper although all model uncertainties are unknown. Thus, the controller can be simple. From the Lyapunov stability theory, it is proved that all errors of the proposed control system remain within the prescribed performance bounds. Finally, the simulation results are presented to demonstrate the performance of the proposed scheme.

• Kyungpook Mathematical Journal
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• 제62권2호
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• pp.229-242
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• 2022

In this paper, we introduce a new subclass of k-uniformly close-to-convex functions with respect to conjugate points. We study characterization, coefficient estimates, distortion bounds, extreme points and radii problems for this class. We also discuss integral means inequality with the extremal functions. Our findings may be related with the previously known results.

• Bulletin of the Korean Mathematical Society
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• 제61권2호
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• pp.317-333
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• 2024

For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S^*_s(𝜑) and C_s(𝜑), respectively, the sharp bound of the n^th Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

• Korean Journal of Mathematics
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• 제32권2호
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• pp.285-295
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• 2024

In this work, we consider the function $${\Psi}(z)=\frac{z}{\ln(1+z)}=1+\sum\limits_{n=1}^{\infty}\,G_nz^n$$ whose coefficients G_n are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass ${\mathcal{G}}^{{\lambda},{\mu}}_{\Sigma}(\Psi)$ of analytic bi-univalent functions subordinate to the function Ψ. For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.183-194
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• 1998

Making use of a certain operator of fractional derivative, a new subclass $L_p({\alpha},{\beta},{\gamma},{\lambda})$) of analytic and p-valent functions is introduced in the present paper. Apart from various coefficient bounds, many interesting and useful properties of this class of functions are given, some of these properties involve, for example, linear combinations and modified Hadamard product of several functions belonging to the class introduced here.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.651-663
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• 2019

In this paper, we introduce and study a new subclass of p-valent harmonic functions defined by modified operator and obtain the basic properties such as coefficient characterization, distortion properties, extreme points, convolution properties, convex combination and also we apply integral operator for this class.

• Honam Mathematical Journal
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• 제39권4호
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• pp.591-601
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• 2017

In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

• Bulletin of the Korean Mathematical Society
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• 제36권4호
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• pp.763-770
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• 1999

The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $$\mid$z$\mid$$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

• Bulletin of the Korean Mathematical Society
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• 제47권2호
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• pp.251-261
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• 2010

This paper deals with a predator-prey model with Holling type III response function and cross-diffusion subject to the homogeneous Neumann boundary condition. We first give a priori estimates (positive upper and lower bounds) of positive steady states. Then the non-existence and existence results of non-constant positive steady states are given as the cross-diffusion coefficient is varied, which means that stationary patterns arise from cross-diffusion.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.123-130
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• 2005

In this paper we discuss a class of analytic functions related to the starlike functions in the unit disk. We prove that this class belongs to the class of close-to-convex functions, we obtain the sharp coefficient upper bounds and distortion theorem of this class, we also get the convexity radius of this class.