Strong Convergence Theorems of Common Elements for Equilibrium Problems and Fixed Point Problems in Banach Spaces
查看参考文献28篇
文摘
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In this paper,we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-φ-non-expansive mappings and the set of solutions of an equilibrium problem.We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K). |
来源
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Acta Mathematicae Applicatae Sinica-English Series
,2012,28(2):337-350 【核心库】
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DOI
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10.1007/s10255-012-0148-4
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关键词
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strong convergence
;
projection
;
quasiφ-nonexpansive mapping
;
common elements
;
the property (K)
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地址
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1.
College of Mathematics and Computer Science, Yanan University, Yanan, 716000
2.
Department of Mathematics, Shijiazhuang Mechanical Engineering University, Shijiazhuang, 050003
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语种
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英文 |
文献类型
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研究性论文 |
ISSN
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0168-9673 |
学科
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数学 |
基金
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国家自然科学基金
;
Scientific Research Program Funded by Shaanxi Provincial Education Department
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文献收藏号
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CSCD:4524610
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参考文献 共
28
共2页
|
1.
Alber Ya I. Metric and generalized projection operators in Banach spaces: properties and applications.
Theory and Applications of Nonlinear Operators of Accretive and Monotone Type,1996:15-50
|
CSCD被引
18
次
|
|
|
|
2.
Alber Ya I. An iterative method for solving a class of nonlinear operator equations in Banach spaces.
Panamer. Math. J.,1994,4:39-54
|
CSCD被引
1
次
|
|
|
|
3.
Bauschke H H. The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space.
J. Math. Anal. Appl.,1996,202:150-159
|
CSCD被引
16
次
|
|
|
|
4.
Bauschke H H. On projection algorithms for solving convex feasibility problems.
SIAM Rev.,1996,38:367-342
|
CSCD被引
39
次
|
|
|
|
5.
Blum E. From optimization and variational inequalities to equilibrium problems.
Math. Student,1994,63:123-145
|
CSCD被引
19
次
|
|
|
|
6.
Browder F E. Fixed point theorems for noncompact mappings in Hilbert spaces.
Proc. Natl. Acad. Sci. USA,1965,53:1272-1276
|
CSCD被引
10
次
|
|
|
|
7.
Butnariu D. Asymptotic behavior of relatively nonexpansive operators in Banach spaces.
J. Appl. Anal.,2001,7:151-174
|
CSCD被引
10
次
|
|
|
|
8.
Butnariu D. Weak convergence of orbits of nonlinear operators in reflexive Banach spaces.
Numer. Funct. Anal. Optim.,2003,24:489-508
|
CSCD被引
5
次
|
|
|
|
9.
Cho Y J. Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings.
Comput. Math. Appl.,2004,47:707-717
|
CSCD被引
17
次
|
|
|
|
10.
Combettes P L. Equilibrium programms in Hilbert spaces.
J. Nonlinear. Convex Anal.,2005,6:117-136
|
CSCD被引
46
次
|
|
|
|
11.
Halpern B. Fixed points of nonexpanding maps.
Bull. Am. Math. Soc.,1967,73:957-961
|
CSCD被引
50
次
|
|
|
|
12.
Hudzik H. Approximative compactness and full rotundity in Musielak-Orlicz spaces and Lorentz-Orlicz spaces.
Zeitschrift fur Analysis und ihre Anwendungen,2006,25:163-192
|
CSCD被引
14
次
|
|
|
|
13.
Kamimura S. Strong convergence of a proximal-type algorithm in a Banach space.
SIAM J. Optim.,2002,13:938-945
|
CSCD被引
44
次
|
|
|
|
14.
Lions P L. Approximation de points fixes de contractions.
C.R. Acad. Sci. Paris Ser. A-B,1977,284:1357-1359
|
CSCD被引
1
次
|
|
|
|
15.
Martinez-Yanes C. Strong convergence of the CQ method for fixed point iteration processes.
Nonlinear Anal.,2006,64:2400-2411
|
CSCD被引
19
次
|
|
|
|
16.
Matsushita S. A strong convergence theorem for relatively nonexpansive mappings in a Banach space.
J. Approx. Theory,2005,134:257-266
|
CSCD被引
26
次
|
|
|
|
17.
Moudafi A. Second-order differential proximal methods for equilibrium problems.
J. Inequal. Pure Appl. Math.,2003,4(1):art.18
|
CSCD被引
1
次
|
|
|
|
18.
Plubtieng S. Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space.
J. Approx. Theory,2007,149:103-115
|
CSCD被引
6
次
|
|
|
|
19.
Reich S. A weak convergence theorem for the alternating method with Bregman distance.
Theory and Applicationsof Nonlinear Operatorsof Accretive and Monotone Type,1996:313-318
|
CSCD被引
1
次
|
|
|
|
20.
Qin X L. Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces.
J. Comput. Appl. Math.,2009,225:20-30
|
CSCD被引
15
次
|
|
|
|
|