• East Asian mathematical journal
• /
• 제5권1호
• /
• pp.1-23
• /
• 1989

Let $S_p*({\alpha},{\beta},{\mu})$ denote the class of functions $f(z)=z^p-{\sum}{\limit}^{\infty}_{n=1}a_{p+n}\;z^{p+n}(a_{p+n}{\geq}o,\;p{\in}N)$ analytic and p-valent in the unit disc $U=\{z:{\mid}z{\mid}<1\}$ and satisfy the condition $${\mid}\frac{\frac{zf'(z)}{f(z)}-p}{\mu\frac{zf'(z)}{f(z)}+p-(1+\mu)\alpha}\mid<\beta,\;z{\in}U$$, where $o{\leq}{\alpha} and $o\leq\mu\leq1$. Further f(z) is said to belong to the class $C_p*({\alpha},{\beta},{\mu})\;if\;zf'(z)/p{\in}S_p*(\alpha,\beta,\mu)$. In this paper we obtain for these classes sharp results concerning coefficient estimates, disortion theorems, closure theorems, Hadamard products and some distortion theorems for the fractional calculus.

• East Asian mathematical journal
• /
• 제5권1호
• /
• pp.57-67
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제29권3_4호
• /
• pp.921-936
• /
• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• East Asian mathematical journal
• /
• 제4권
• /
• pp.57-73
• /
• 1988

The subclasses S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) ($0\leqq\alpha<1,\;0<\beta\leqq1$ and $0\leqq\mu\leqq1$) of T the class of analytic and univalent functions of the form $$f(z)=z-\sum\limit^{\infty}_{n=2}\mid a_n\mid z^n$$ have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) are determined along with a representation formula for the functions in S*($\alpha,\beta,\mu$). Furthermore, it is shown that the classes S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) are closed under arithmetic mean and convex linear combinations. Also in this paper, we find extreme points and support points for these classes.

• Kyungpook Mathematical Journal
• /
• 제59권3호
• /
• pp.415-431
• /
• 2019

In this paper we introduce a new class of operators which will be called the class of k-quasi-class A(s, t) operators. An operator $T{\in}B(H)$ is said to be k-quasi-class A(s, t) if $$T^{*k}(({\mid}T^*{\mid}^t{\mid}T{\mid}^{2s}{\mid}T^*{\mid}^t)^{\frac{1}{t+s}}-{\mid}T^*{\mid}^{2t})T^k{\geq}0$$, where s > 0, t > 0 and k is a natural number. We show that an algebraically k-quasi-class A(s, t) operator T is polaroid, has Bishop's property ${\beta}$ and we prove that Weyl type theorems for k-quasi-class A(s, t) operators. In particular, we prove that if $T^*$ is algebraically k-quasi-class A(s, t), then the generalized a-Weyl's theorem holds for T. Using these results we show that $T^*$ satisfies generalized the Weyl's theorem if and only if T satisfies the generalized Weyl's theorem if and only if T satisfies Weyl's theorem. We also examine the hyperinvariant subspace problem for k-quasi-class A(s, t) operators.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제10권4호
• /
• pp.265-271
• /
• 2003

Let $CS_\alpha(\beta)$ denote the class of normalized strongly $\alpha$-close-to-convex functions of order $\beta$, defined in the open unit disk $\cal{U}$ of $\mathbb{C}$${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$ such that $g\; \in\;S^{\ask}$, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to $CS_\alpha(\beta)$.

• East Asian mathematical journal
• /
• 제21권2호
• /
• pp.233-240
• /
• 2005

Let $CS^{\alpha}(\beta)$ denote the class of normalized strongly $\alpha$-logarithmic close-to-convex functions of order $\beta$, defined in the open unit disk $\mathbb{U}$ by $$\|arg\{\(\frac{f(z)}{g(z)}\)^{1-\alpha}\(\frac{zf'(z)}{g(z)\)^{\alpha}\}\|\leq\frac{\pi}{2}\beta,\;(\alpha,\beta\geq0)$$ where $g{\in}S^*$ the class of normalized starlike functions. In this paper, we prove sharp $Fekete-Szeg\"{o}$ inequalities for functions $f{\in}CS^{\alpha}(\beta)$.

• 대한수학회지
• /
• 제60권1호
• /
• pp.195-212
• /
• 2023

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator 𝓜_ϕ,β are established. Meanwhile, we introduce the ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ conditions and obtain the characterization of two-weighted inequalities for 𝓜_ϕ,β. Finally, the relationships of the conditions ${\mathcal{S}}_{({\vec{p}},q),{\beta}}({\varphi}),\,{\mathcal{A}}_{({\vec{p}},q),{\beta}}({\varphi})$ and $B_{({\vec{p}},q),{\beta}}({\varphi})$ and the characterization of the one-weight $A_{({\vec{p}},q),{\beta}}({\varphi})$ are given.

• Journal of the Korean Statistical Society
• /
• 제31권4호
• /
• pp.459-468
• /
• 2002

A class of asymmetric beta-ARCH processes is proposed and connections to traditional ARCH models are explained. Geometric ergodicity of the model is discussed. Conditional least squares as well as maximum likelihood estimators of parameters and their limit results are also presented. A test for symmetry of the model is studied with limiting power of test statistic given.

• 미생물학회지
• /
• 제34권4호
• /
• pp.194-199
• /
• 1998

한강의 본류와 만나는 탄천과 중랑천에서 16S rDAN를 증폭하고 부분적인 염기서열 분석을 통하여 한강의 세균 다양성을 결정하였다. 총 27개의 클론을 분리하였으며 RFLP를 이용하여 7개의 group으로 나누었다. 탄천의 15개 클론은 4개의 group으로 나뉘어졌으며 가장 많은 클론을 포함하는 group(HT-1 클론)은 class Proteobacteria의 ${\delta}$-subdivision에 속하는 Acrobacter cryaerophilius와 높은 유사도를 보였으며, 다른 두 group(HT-6과 HT-9 클론)은 모두 clas Cytophagales에 속하였다. 중랑천의 12개의 클론은 3개의 group으로 나뉘어졌으며 가장 많은 클론을 보이는 group(HJ-1 클론)은 class Proteobacteria의 ${\alpha}$-subdivision에 속하는 Sphingomonas sp. 와 높은 유사도를 나타내었다. 전체적으로는 Proteobateria(alpha, beta and delta subdivision), Cytophagales와 Actinomycetales가 검출되었다.