• 대한수학회지
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• 제41권2호
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• pp.243-248
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• 2004

In this note, we get some generalized KKM theorems for the k-set contraction mapping on the nearly-convex sets.

• East Asian mathematical journal
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• 제24권4호
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• pp.339-345
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• 2008

Some equivalence conditions for the convergence of iterative sequences for set-valued contraction mapping in Banach spaces are obtained.

• 대한수학회지
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• 제45권6호
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• pp.1725-1740
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• 2008

In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.

• 대한수학회지
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• 제34권1호
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• pp.237-245
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• 1997

The fixed point index plays an important role in solving the positive solutions of nonlinear equations in ordered Banach spaces ([7], [10], [11], [14], [15]). Many authors have studied the existence problems of positive solutions of nonlinear equations for nonlinear mappings ([1]-[5], [7], [9], [10], [14], [15]).

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1445-1460
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• 2010

In this paper, a second-order system of multi-point boundary value problems in Banach spaces is investigated. Based on a specially constructed cone and the fixed point theorem of strict-set-contraction operators, the criterion of the existence and multiplicity of positive solutions are established. And two examples demonstrating the theoretic results are given.

• 대한수학회지
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• 제46권3호
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• pp.561-576
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• 2009

We introduce two iterative algorithms for finding a common element of the set of fixed points of an asymptotically k-strict pseudo-contraction and the set of solutions of a mixed equilibrium problem in a Hilbert space. We obtain some weak and strong convergence theorems by using the proposed iterative algorithms. Our results extend and improve the corresponding results of Tada and Takahashi [16] and Kim and Xu [8, 9].

• 한국염색가공학회지
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• 제27권4호
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• pp.309-317
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• 2015

This study is the high contraction processing conditions set by the method of the CPB process. And the ultimate goal of this study is the high contraction of the CPB processing test method that can solve the problems of the high-contraction fabric processing method of the current jet dyeing machine. Non-coating process(CPB process) developed by the expression of a soft touch, light weight, functional and to develop excellent breathable nylon fabric. The nylon fabrics established the optimum processing conditions through the high contraction of the various test conditions, the CPB system.(The benzyl alcohol was used as the main constrictor.) At this time, the warp and weft contraction of nylon fabric was about 20%. And it established the constrictor concentration, the treatment temperature, time of a variety of tests. Also non-coating process(CPB process) can develop soft touch, lightweight, excellent air permeability. As a result, we developed a high contraction nylon fabric having a uniform surface. Manufactured fabric is used for Wind-proof and Down-proof.

• 대한수학회보
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• 제45권1호
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• pp.67-73
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• 2008

The purpose of this paper is to present some fixed point results for nonself multivalued operators on a set with two metrics. In addition, a homotopy result for multivalued operators on a set with two metrics is given. The data dependence and the well-posedness of the fixed point problem are also discussed.

• The Korean Journal of Physiology
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• 제1권1호
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• pp.67-72
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• 1967

Present paper is attempted to introduce the phenomenon of 'after contraction' in isolated cardiac-muscle. Papillary muscles were removed from cat right ventricle and were used as a preparation. The muscle strip was Placed in tissue bath which is kept in steady temperature of around $25^{\circ}C$ and was perfuced by Tyrode solution, saturated with 95% $O_2$ and 5% $CO_2.$ under the condition of high calcium (8.2-10.0 mM/l), low sodium (72.4-70.0 mM/l) perfusion with the administration of epinephrine (1-2 mg/l) into tile tissue bath normally triggered muscle contraction was followed by oscillatory, repetitive contractions - after contraction. The phenomenon of after contraction was augumented by decrease in tissue bath temperature and by increase in number of preceding beats and in driving rate. Authors were able to maintain the phenomenon in prominent and steady state giving proper experimental conditions such as fixed bath temperature (ranged from $22^{\circ}C\;to\;27^{\circ}C$), suitable driving rate (20 per minute in average) and perfusion of high calcium, loll sodium and 1-2 mg/l of epinephrine. In some preparations, the strength of after contraction (second contraction) reached up-to 80% of normally triggered contraction and five repetitive contractions were observed as largest number of after contractions. Intracellular action potential measured in the muscle which was beating regulary showing steady after contraction revealed no oscillating after potential in most parts of the muscle but in few cases oscillating changes of after potentials were detectable. In electrogram of the muscle preparation recorded by means of contact electrode prominent, oscillating after potentials were observable when the recorder was set at highest sensitivity. It still is not clear that whether after contraction is the phenomenon which corresponds to those changes in action potential, oscillating after potential, of the muscle preparation. Possible mechanism of the phenomenon of after contraction relating with after potential changes was proposed. Detailed results obtained from further studies on after contraction and concrete discussion on the phenomenon will be reported by authors.

• Korean Journal of Mathematics
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• 제20권2호
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• pp.225-237
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• 2012

In this paper, we introduce a new iterative scheme to investigate the problem of nding a common element of nonexpansive mappings and the set of solutions of generalized variational inequalities for a $k$-strict pseudo-contraction by relaxed extra-gradient methods. Strong convergence theorems are established in $q$-uniformly smooth Banach spaces.