• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.550-554
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• 1992

In this paper the issue of convergence rate is introduced for a learning control scheme we have developed and applied for tracking of unknown linear systems. A sufficient condition under which the output trajectory converges exponentially fast is obtained using the controllability grammian of controllable linear systems. Under the same condition it is also shown that the learning control input converges exponentially with the same rate as the rate of output convergence. A numerical example with computer simulation results is presented to show the feasibility of the scheme.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• 대한수학회보
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• 제49권4호
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.399-416
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• 2013

The semilocal convergence of a third order iterative method used for solving nonlinear operator equations in Banach spaces is established by using recurrence relations under the assumption that the second Fr´echet derivative of the involved operator satisfies the ${\omega}$-continuity condition given by $||F^{\prime\prime}(x)-F^{\prime\prime}(y)||{\leq}{\omega}(||x-y||)$, $x,y{\in}{\Omega}$, where, ${\omega}(x)$ is a nondecreasing continuous real function for x > 0, such that ${\omega}(0){\geq}0$. This condition is milder than the usual Lipschitz/H$\ddot{o}$lder continuity condition on $F^{\prime\prime}$. A family of recurrence relations based on two constants depending on the involved operator is derived. An existence-uniqueness theorem is established to show that the R-order convergence of the method is (2+$p$), where $p{\in}(0,1]$. A priori error bounds for the method are also derived. Two numerical examples are worked out to demonstrate the efficacy of our approach and comparisons are elucidated with a known result.

• 대한수학회보
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• 제39권2호
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• pp.269-276
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• 2002

Let E be a real Banach space. Let T : E longrightarrow E be a map with F(T) : = { x $\in$ E : Tx = x} $\neq$ 0 and satisfying the accretive-type condition $\lambda\$\mid$x-Tx\$\mid$^2$, for all $x\inE,\;x^*\inf(T)\;and\;\lambda >0$. We prove some necessary and sufficient conditions for the convergence of the Mann iterative sequence to a fixed point of T.

• 한국산업융합학회 논문집
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• 제3권3호
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• pp.201-207
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• 2000

In this study, methodologies for checking the interference between in-core instrumentation (ICI) guide tubes for routing of ICI guide tubes in the reactor coolant system of typical Pressurized Water Reactor under cold and normal operation (NOP) conditions are presented. The closest points of ICI guide tubes under cold condition are calculated by using minimize technique and are used as data for NOP analysis. Movements of ICI guide tubes under NOP condition are performed by the commercial computer code, SUPERPIPE.

• 대한수학회논문집
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• 제37권2호
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• pp.415-421
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• 2022

This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M_α-integral using the M_α-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M_α-strong Lusin condition was imposed.

• Composites Research
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• 제29권4호
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• pp.216-222
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• 2016

폴리디싸이클로팬타디엔 (p-DCPD) 수지를 경화하기 위해 개환반응이 사용된다. 이 반응은 텅스텐계 촉매를 이용한 반응이기 때문에 질소 조건에서 반응이 진행되어야 한다. 왜냐하면, 텅스텐계 수지는 촉매독 현상이 발생될 수 있기 때문에 대기조건에서는 사용이 어려운 것으로 알려져 있다. 이러한 문제를 개선하기 위해 본 연구에서는 대기 조건에서 텅스턴 (W)을 촉매로한 p-DCPD 대해 프레스 성형법을 이용하여 수지를 경화시켰다. 프레스 성형을 통해 p-DCPD (W) 수지를 경화시킬 경우 기계적 강도가 향상되는 결과를 얻었으며, 이는 DCPD 성형 단계에서 발생되는 기체를 압으로 눌러 미세 기공의 발생을 줄였기 때문이다. 촉매 독 현상이 발생되는 것은 반응시간이 길 때에 발생되지만, 짧은 성형을 시도하는 프레스 성형에서는 촉매 자체로 인한 물성 저하가 발생되지 않았다. 궁극적으로 p-DCPD 성형을 위해 대기 조건에서 성형이 가능하였으며, 경화 시간, 압력 변수를 조절할 경우 기계적 물성이 향상을 확인하였다.

• 한국산업융합학회 논문집
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• 제14권2호
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• pp.73-78
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• 2011

Power consumption for wire gauge impeller in cylindrical agitated vessel was measured over a wide range of Reynolds number from laminar to turbulent flow regions. The power correlation were obtained agitation power input of WM4 at gassing condition in turbulent region, at gassing condition in transient region and at gassing condition in laminar region. Also the compared with effect of impeller diameter and blade width on agitation power input at gassing condition in turbulent region, at gassing condition in transient region and at gassing condition in laminar region.