In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution s...In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.展开更多
It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper pro...It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence.展开更多
Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in th...Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in this paper provides a convergence rate estimate. Moreover the resultin this paper improves,generalizes and summarizes some important and el- egant recent results展开更多
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu...In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].展开更多
This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combi...This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.展开更多
In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which exten...In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.展开更多
在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c...在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.展开更多
In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the mod...In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.展开更多
In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a sem...In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.展开更多
The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a...The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67（7）, 2258-2271 （2007）], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 （2006）], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 （2006）], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 （2003）], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329（1）, 336-346 （2007）], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 （2007）], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26（11）, 1835-1842 （1996）], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12（2）, 77-88 （2002）], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 （2007）].展开更多
The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontract...The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in the Hilbert space. The presented results extend and improve the corresponding results reported in the lit-erature.展开更多
The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive ...The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others.展开更多
基金supported by National Research Foundation of Korea Grantfunded by the Korean Government (2009-0076898)
文摘In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.
基金Supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Ed-ucation Institutions of MOE,P.R.C.
文摘It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure.The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence.
基金This project was supported both by the National Natural Science Foundation of China (1 980 1 0 2 3 ) andby the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institu-tions of MOEP.R.C.
文摘Itis shown that any fixed point of each Lipschitzian,strictly pseudocontractive map- ping T on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure.The argument in this paper provides a convergence rate estimate. Moreover the resultin this paper improves,generalizes and summarizes some important and el- egant recent results
基金supported by Scientific Research Fund of Sichuan Provincial Education Department (09ZB102)Scientific Research Fund of Science and Technology Deportment of Sichuan Provincial (2011JYZ011)
文摘In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].
文摘This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.
文摘In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.
文摘在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.
基金Scientific Research Fund of Zhejiang Provincial Education Department(No.20051778 and No.20051760)Scientific Research Fund of Ningbo University(200542)
文摘In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.
基金Supported by the National Natural Science Foundation of China (Grant No.10271035)the Scientific Research Foundation Project of Inner Mongolian Education Department (Grant No.NJ06088)
文摘In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.
基金Supported by Natural Science Foundation of Yibin University （Grant No. 2007Z3）
文摘The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67（7）, 2258-2271 （2007）], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 （2006）], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 （2006）], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 （2003）], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329（1）, 336-346 （2007）], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 （2007）], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26（11）, 1835-1842 （1996）], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12（2）, 77-88 （2002）], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 （2007）].
基金supported by the Sichuan Educational Committee Science Foundation for Youths (No. 08ZB002) the Natural Science Foundation of Sichuan Province (No. 2008ZC001)
文摘The main purpose of this paper is to study a new iterative algorithm for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in the Hilbert space. The presented results extend and improve the corresponding results reported in the lit-erature.
基金Research Foundation of Henan University (No.06YBZR034)
文摘The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others.
基金supported by the National Natural Science Foundation of China(10771050)Scientific Research Program Fundedby Shaanxi Provincial Education Department(11JK0486)~~
