The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e...The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.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, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presen...In this paper, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.： Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 （2007）]. In order to get a strong convergence theorem, we modify the normal Mann＇s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.： Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51- 60 （2005）] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.展开更多
In this paper,we introduce a general hybrid iterative method to find an infinite family of strict pseudo-contractions in a q-uniformly smooth and strictly convex Banach space.Moreover,we show that the sequence defined...In this paper,we introduce a general hybrid iterative method to find an infinite family of strict pseudo-contractions in a q-uniformly smooth and strictly convex Banach space.Moreover,we show that the sequence defined by the iterative method converges strongly to a common element of the set of fixed points,which is the unique solution of the variational inequality<(λφ−νF)z,jq(z−z)>≤0,for z∈⋂_(i=1)^(∞)Γ(S_(i)).The results introduced in our work extend to some corresponding theorems.展开更多
基金supported by the Natural Science Foundation of Yibin University (No. 2007Z3)
文摘The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
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.
基金Supported by National Natural Science Foundation of China (Grant No. 10771050)
文摘In this paper, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.： Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 （2007）]. In order to get a strong convergence theorem, we modify the normal Mann＇s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.： Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51- 60 （2005）] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.
基金supported by the National Natural Science Foundation of China(12001416,11771347 and 12031003)the Natural Science Foundations of Shaanxi Province(2021JQ-678).
文摘In this paper,we introduce a general hybrid iterative method to find an infinite family of strict pseudo-contractions in a q-uniformly smooth and strictly convex Banach space.Moreover,we show that the sequence defined by the iterative method converges strongly to a common element of the set of fixed points,which is the unique solution of the variational inequality<(λφ−νF)z,jq(z−z)>≤0,for z∈⋂_(i=1)^(∞)Γ(S_(i)).The results introduced in our work extend to some corresponding theorems.
基金supported by the National Natural Science Foundation of China(10771050)Scientific Research Program Fundedby Shaanxi Provincial Education Department(11JK0486)~~
