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Convergence theorems for inverse-strongly monotone mappings and quasi-Φ-nonexpansive mappings
Xiaolong Qin,강신민,조열제 대한수학회 2009 대한수학회보 Vol.46 No.5
In this paper, we consider a hybrid projection algorithm for a pair of inverse-strongly monotone mappings and a quasi-Φ-nonexpansive mapping. Strong convergence theorems are established in the framework of Banach spaces.
CONVERGENCE THEOREMS FOR INVERSE-STRONGLY MONOTONE MAPPINGS AND QUASI-φ-NONEXPANSIVE MAPPINGS
Qin, Xiaolong,Kang, Shin-Min,Cho, Yeol-Je Korean Mathematical Society 2009 대한수학회보 Vol.46 No.5
In this paper, we consider a hybrid projection algorithm for a pair of inverse-strongly monotone mappings and a quasi-$\phi4-nonexpansive mapping. Strong convergence theorems are established in the framework of Banach spaces.
Xiaolong Qin,Yongfu Su,Meijuan Shang 대한수학회 2008 대한수학회지 Vol.45 No.1
In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others. In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.
Qin, Xiaolong,Su, Yongfu,Shang, Meijuan Korean Mathematical Society 2008 대한수학회지 Vol.45 No.1
In this paper, we introduce a modified three-step iteration scheme with errors for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. We then use this scheme to approximate a common fixed point of these mappings. The results obtained in this paper extend and improve the recent ones announced by Khan, Fukhar-ud-di, Zhou, Cho, Noor and some others.
Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods
Qin, Xiaolong,Su, Yongfu,Shang, Meijuan Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.1
In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.
김종규,Xiaolong Qin,임원희 영남수학회 2012 East Asian mathematical journal Vol.28 No.5
In this paper, the problem of iterative approximation of com- mon fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are estab- lished. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.
조열제,강신민,Xiaolong Qin 대한수학회 2010 대한수학회보 Vol.47 No.6
In this paper, we consider an implicit iterative process with errors for an infinite family of strict pseudocontractions. Strong convergence theorems are established in the framework of Banach spaces. The results presented in this paper improve and extend the recent ones announced by many others.
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.
A system of nonlinear variational inclusions with (A, η)-monotone mappings in Hilbert spaces
Meijuan Shang,Xiaolong Qin 영남수학회 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we introduce a system of nonlinear variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.