• Title, Summary, Keyword: extreme points

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ON CLOSED CONVEX HULLS AND THEIR EXTREME POINTS

  • Lee, S.K.;Khairnar, S.M.
    • Korean Journal of Mathematics
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    • v.12 no.2
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    • pp.107-115
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    • 2004
  • In this paper, the new subclass denoted by $S_p({\alpha},{\beta},{\xi},{\gamma})$ of $p$-valent holomorphic functions has been introduced and investigate the several properties of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$. In particular we have obtained integral representation for mappings in the class $S_p({\alpha},{\beta},{\xi},{\gamma})$) and determined closed convex hulls and their extreme points of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$.

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Extreme spirallike products

  • Lee, Suk-Young;David Oates
    • Communications of the Korean Mathematical Society
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    • v.10 no.4
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    • pp.875-880
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    • 1995
  • Let $S_p(\alpha)$ denote the class of the Spirallike functions of order $\alpha, 0 < $\mid$\alpha$\mid$ < \frac{\pi}{2}$ Let $\Pi_N$ denote the subset of $S_p(\alpha)$ consisting of all products $z\Pi^N_{j=1}(1-u_j z)^{-mt_j}$ where $m = 1 + e^{-2i\alpha},$\mid$u_j$\mid$ = 1, t_j > 0$ for $j = 1, \cdots, N$ and $\sum^{N}_{j=1}{t_j = 1}$. In this paper we prove that extreme points of $S_p(\alpha)$ may be found which lie in $\Pi_N$ for some $N \geq 2$. We are let to conjecture that all exreme points of $S_p(\alpha)$ lie in $\Pi_N$ for somer $N \geq 1$ and that every such function is an extreme point.

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THE UNIT BALL OF THE SPACE OF BILINEAR FORMS ON ℝ3 WITH THE SUPREMUM NORM

  • Kim, Sung Guen
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.487-494
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    • 2019
  • We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ which leads to a complete formula of ${\parallel}f{\parallel}$ for every $f{\in}{\mathcal{L}}(^2l^3_{\infty})^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ is exposed.

EXTREME POINTS RELATED TO MATRIX ALGEBRAS

  • Lee, Tae Keug
    • Korean Journal of Mathematics
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    • v.9 no.1
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    • pp.45-52
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    • 2001
  • Let A denote the set {$a{\in}M_n{\mid}a{\geq}0$, $tr(a)=1$}, $St(M_n)$ the set of all states on $M_n$, and $PS(M_n)$ the set of all pure states on $M_n$. We show that there are one-to-one correspondences between A and $St(M_n)$, and between the set of all extreme points of A and $PS(M_n)$. We find a necessary and sufficient condition for a state on $M_{n1}{\oplus}{\cdots}{\oplus}M_{nk}$ to be extended to a pure state on $M_{n1}+{\cdots}+_{nk}$.

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Extremal Problems for 𝓛s(22h(w))

  • Kim, Sung Guen
    • Kyungpook Mathematical Journal
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    • v.57 no.2
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    • pp.223-232
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    • 2017
  • We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms. We also show that every extreme symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms is exposed.

LOCAL STRUCTURE OF TRAJECTORY FOR EXTREMAL FUNCTIONS

  • Lee, Suk-Young
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.609-619
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    • 1999
  • IN this note we study more about the omitted are for the extremal functions and its {{{{ {π } over {4 } }}}}-property based upon Schiffer's variational method and zBrickman-Wilken's result. we give an example other than the Koebe function which is both a support point of S and the extreme point of HS. Furthermore, we discuss the relations between the support points and the L wner chain.

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