http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
WEAK AND STRONG CONVERGENCE TO COMMON FIXED POINTS OF NON-SELF NONEXPANSIVE MAPPINGS
Su, Yongfu,Qin, Xiaolong 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.
Projection methods for relaxed cocoercive variation inequalities in Hilbert spaces
Yongfu Su,HONG ZHANG 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper, we introduce and consider a new system of re- laxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the pro- jection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this pa- per extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear vari- ational inequalities with different (γ, r)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032]. In this paper, we introduce and consider a new system of re- laxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the pro- jection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this pa- per extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear vari- ational inequalities with different (γ, r)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].
PROJECTION METHODS FOR RELAXED COCOERCIVE VARIATION INEQUALITIES IN HILBERT SPACES
Su, Yongfu,Zhang, Hong The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper, we introduce and consider a new system of relaxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the projection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this paper extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed co coercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different ($\gamma,r$)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].
Su, Yongfu,Wang, Xiuzhen,Gao, Junyu The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.1
The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.
Yongfu Su,Xiuzhen Wang,Junyu Gao 영남수학회 2008 East Asian mathematical journal Vol.24 No.1
The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.
Hong Zhang,Yongfu Su,Mengqin Li 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
T.H. Kim, H.K. Xu, [Convergence of the modified Mann’s it- eration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:10.1016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo- contractions. In the proved process of this paper,Cauchy sequencesmethod is used, so we complete the proof without using the demi-closedness prin- ciple, Opial’s condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T ) is bounded. On the other hand, we relax the restriction on the control se- quence of iterative scheme. T.H. Kim, H.K. Xu, [Convergence of the modified Mann’s it- eration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:10.1016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo- contractions. In the proved process of this paper,Cauchy sequencesmethod is used, so we complete the proof without using the demi-closedness prin- ciple, Opial’s condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T ) is bounded. On the other hand, we relax the restriction on the control se- quence of iterative scheme.
Guanghui Gu,Yongfu Su 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1
The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117 ].
STRONG CONVERGENCE OF MODIFIED HYBRID ALGORITHM FOR QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
Zhang, Huancheng,Su, Yongfu Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.4
In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-$\phi$-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.
Ziming Wang,Yongfu Su 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
We introduce a new iterative algorithm for equilibrium and fixed point problems of three hemi-relatively nonexpansive mappings by the CQ hybrid method in Banach spaces, Our results improve and extend the corresponding results announced by Xiaolong Qin, Yeol Je Cho, Shin Min Kang [Xiaolong Qin, Yeol Je Cho, Shin Min Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, Journal of Computational and Applied Mathematics 225(2009) 20-30], P. Kumam, K. Wattanawitoon [P. Kumam, K. Wattanawitoon, Convergence theorems of a hybrid algorithm for equilibrium problems, Nonlinear Analysis: Hybrid Systems (2009),doi:10.1016/j.nahs.2009.02.006], W. Takahashi, K. Zembayashi [W. Takahashi, K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008) doi:10.1155 /2008/528476]and others therein.