• Korean Journal of Mathematics
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• v.16 no.2
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• pp.215-231
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• East Asian mathematical journal
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• v.24 no.1
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• (The) Research of the performance art and culture
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• no.23
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• pp.185-212
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• 2011

Buddhist dance (seungmu) is a crux and highlight of Korean traditional dance; its aesthetics and technique are extraordinary, and Korean dance's unique style is well expressed. The Buddhist dance, which has been descended, is divided into Han Yeong Suk style, which is designated as Important Intangible Asset Number 27, and Lee Mae Bang style. While the two dances are same one, area is difference and they have unique style because of genealogical difference. However, studies on Buddhist dance so far have focused on single style's dance, or comparison of regional aspects (Han Yeong Suk dance is from Gyeonggi and Lee Mae Bang dance is from Honam area). But, Lee Byeong Ok suggested traditional artist dance is differed by male dance genealogy and female dance (gibang) genealogy dance, and while folk dance has storng tie with region, but artist dance has weak regional tie. Therefore, the purpose of this thesis is to study genealogical character of Buddhist dance's dancing style, clarifying Han Yeong Suk dance is male dance genealogy and Lee Mae Bang dance is gibang dance genealogy. In other words, among three theses that compared Lee Mae Bang and Han Yeong Suk dances, one analyzing movement, one comparing dance of invocation and one comparing traditional ballad, are re-analyzed from genealogical perspective and characteristics are comparatively analzyed. The overall summary of the genealogical attitude of the Han Yeong Suk and Lee Mae Ban dances is; First, Han's dance has masculinity, upwardness, progressiveness, activeness, outgoing character, boldness and grace, which are character of male dance lineage, while Lee's dance shows feminity, downwardness, backwardness, aesthecity, inwardness, delicacy and coquette. Second, the most expressed parts of the attitude of two dances are genealogical character, and then are original and regional characters. Third, two dances have strong genealogical attitude, but also has anti-genealogical attitude since the gender of descendent was changed, in other words Lee Mae Bang was man, and Han Yeong Suk was woman. Fourth, even though the two Buddhist dances have different genealogy and region, they share similarities as traditional dance descended in the same time period, so there are many common features. In other words, the two dances are Korean nation's dance and from same time period, but they should not be mixed, either. Even though they have small differences, they must keep each genealogy and descend to the next generation.