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- 저자 : Yisheng Song (검색결과 10 건)
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Song, Yisheng,Chen, Rudong Korean Mathematical Society 2008 대한수학회지 Vol.45 No.5
Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.
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New iterative algorithms for zeros of accretive operators
Yisheng Song 대한수학회 2009 대한수학회지 Vol.46 No.1
Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly Gateaux differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also. Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly Gateaux differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also.
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Yisheng Song,Rudong Chen 대한수학회 2008 대한수학회지 Vol.45 No.5
Let K be a nonempty closed convex subset of a Banach space E. Suppose {Tn} (n = 1, 2, . . .) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ∩∞n=1 F(Tn) ≠0. For x0 ∈ K, define xn+1 = λn+1xn + (1 − λn+1)Tn+1xn, n ≥ 0. If λn ⊂ [0, 1] satisfies limn→∞ λn = 0, we proved that {xn} weakly converges to some z ∈ F as n → ∞ in the framework of reflexive Banach space E which satisfies the Opial’s condition or has Fr´echet differentiable norm or its dual E* has the Kadec-Klee property. We also obtain that {xn} strongly converges to some z ∈ F in Banach space E if K is a compact subset of E or there exists one map T ∈ {Tn; n = 1, 2, . . .} satisfy some compact conditions such as T is semicompact or satisfy Condition A or limn→∞ d(xn, F(T)) = 0 and so on. Let K be a nonempty closed convex subset of a Banach space E. Suppose {Tn} (n = 1, 2, . . .) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ∩∞n=1 F(Tn) ≠0. For x0 ∈ K, define xn+1 = λn+1xn + (1 − λn+1)Tn+1xn, n ≥ 0. If λn ⊂ [0, 1] satisfies limn→∞ λn = 0, we proved that {xn} weakly converges to some z ∈ F as n → ∞ in the framework of reflexive Banach space E which satisfies the Opial’s condition or has Fr´echet differentiable norm or its dual E* has the Kadec-Klee property. We also obtain that {xn} strongly converges to some z ∈ F in Banach space E if K is a compact subset of E or there exists one map T ∈ {Tn; n = 1, 2, . . .} satisfy some compact conditions such as T is semicompact or satisfy Condition A or limn→∞ d(xn, F(T)) = 0 and so on.
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COINCIDENCE POINTS OF WEAKLY COMPATIBLE MAPPINGS
Song, Yisheng Korean Mathematical Society 2008 대한수학회보 Vol.45 No.4
We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.
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SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS
Song, Yisheng,Cho, Yeol-Je Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838-844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {$x_n$} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.
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Coincidence points of weakly compatible mappings
Yisheng Song 대한수학회 2008 대한수학회보 Vol.45 No.4
We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature. We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.
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NEW ITERATIVE ALGORITHMS FOR ZEROS OF ACCRETIVE OPERATORS
Song, Yisheng Korean Mathematical Society 2009 대한수학회지 Vol.46 No.1
Two new iterative algorithms are provided to find zeros of accretive operators in a Banach space E with a uniformly $G\hat{a}teaux$ differentiable norm. Strong convergence for two iterations is proved and as applications, the viscosity approximation results are obtained also.
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Some notes on Ishikawa iteration for multi-valued mappings
Yisheng Song,조열제 대한수학회 2011 대한수학회보 Vol.48 No.3
In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838--844], the authors introduced several Ishikawa iterative schemes for fixed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {x_n} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.
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Development of a Current-Sensorless Multi-Loop Control for Standalone PWM Inverters
Yuan Yisheng,Liuchen Chang,Song Pinggang 전력전자학회 2007 ICPE(ISPE)논문집 Vol.- No.-
A current-sensorless multi-loop control method that estimates the capacitor current is proposed for standalone inverter applications. The theory of the control loop is given, and a mathematical model is analyzed. The effect of capacitor parameter mismatch on system characteristics was emphasized and discussed through modeling and simulation. Finally, experimental results comparing the characteristics of the output voltage under parameter mismatch conditions verified the operation and merits of the proposed controller.
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An iteration schemes for nonexpansive mappings and variational inequalities
Hongjun Wang,Yisheng Song 대한수학회 2011 대한수학회보 Vol.48 No.5
An iterative algorithm is provided to find a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality in a Hilbert space. Using this result, we consider a strong convergence result for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping. Our results include the previous results as special cases and can be viewed as an improvement and refinement of the previously known results.
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