STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

doi:10.1016/S0252-9602(16)30096-0

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1641-1650.doi: 10.1016/S0252-9602(16)30096-0

STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

张石生¹, 王林², 秦丽娟³, 马招丽⁴

1. Center for General Education, China Medical University, Taichung 40402, China;
2. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China;
3. Department of Mathematics, Kunming University, Kunming 650214, China;
4. School of Information Engineering, College of Arts and Science Yunnan Normal University, Kunming 650222, China

收稿日期:2015-07-17 修回日期:2016-04-18 出版日期:2016-12-25 发布日期:2016-12-25
通讯作者: Shisheng ZHANG,E-mail:changss2013@163.com E-mail:changss2013@163.com
作者简介:Lin WANG,E-mail:wl64mail@aliyun.com;Lijuan QIN,E-mail:annyqlj@163.com;Zhaoli MA,E-mail:kmszmzl@126.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11361070) and the Natural Science Foundation of China Medical University, Taiwan.

STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

Shisheng ZHANG¹, Lin WANG², Lijuan QIN³, Zhaoli MA⁴

1. Center for General Education, China Medical University, Taichung 40402, China;
2. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China;
3. Department of Mathematics, Kunming University, Kunming 650214, China;
4. School of Information Engineering, College of Arts and Science Yunnan Normal University, Kunming 650222, China

Received:2015-07-17 Revised:2016-04-18 Online:2016-12-25 Published:2016-12-25
Contact: Shisheng ZHANG,E-mail:changss2013@163.com E-mail:changss2013@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11361070) and the Natural Science Foundation of China Medical University, Taiwan.

摘要/Abstract

摘要：

The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility problems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new.

关键词: the split equality variational inclusion problem in Banach space, split feasibility problem in Banach space, split equilibrium problem in Banach spaces

Abstract:

Key words: the split equality variational inclusion problem in Banach space, split feasibility problem in Banach space, split equilibrium problem in Banach spaces

中图分类号:

47J25

张石生, 王林, 秦丽娟, 马招丽. STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES[J]. 数学物理学报(英文版), 2016, 36(6): 1641-1650.

Shisheng ZHANG, Lin WANG, Lijuan QIN, Zhaoli MA. STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES[J]. Acta mathematica scientia,Series B, 2016, 36(6): 1641-1650.

参考文献

[1] Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms, 1994, 8:221-239
[2] Byrne C. Iterative oblique projection onto convex subsets and the split feasibility problem. Inverse Problem, 2002, 18:441-453
[3] Censor Y, Bortfeld T, Martin N, Trofimov A. A unified approach for inversion problem in intensitymodulated radiation therapy. Phys Med Biol, 2006, 51:2353-2365
[4] Censor Y, Elfving T, Kopf N, Bortfeld T. The multiple-sets split feasiblility problem and its applications. Inverse Problem, 2005, 21:2071-2084
[5] Censor Y, Motova A, Segal A. Perturbed projections ans subgradient projiections for the multiple-sets split feasibility problem. J Math Anal Appl, 2007, 327:1244-1256
[6] Xu H K. A variable Krasnosel'skii-Mann algorithm and the multiple-sets split feasibility problem. Inverse Problem, 2006, 22:2021-2034
[7] Yang Q. The relaxed CQ algorithm for solving the split feasibility problem. Inverse Problem, 2004, 20:1261-1266
[8] Zhao J, Yang Q. Several solution methods for the split feasibility problem. Inverse Problem, 2005, 21:1791-1799
[9] Chang S S, Cho Y J, Kim J K, Zhang W B, Yang L. Multiple-set split feasibility problems for asymptotically strict pseudocontractions. Abst Appl Anal, 2012, 2012:Article ID 491760
[10] Chang S S, Wang L, Tang Y K, Yang L. The split common fixed point problem for total asymptotically strictly pseudocontractive mappings. J Appl Math, 2012, 2012:Article ID 385638
[11] Moudafi A. A relaxed alternating CQ algorithm for convex feasibility problems. Nonlinear Anal, 2013, 79:117-121
[12] Moudafi A, Al-Shemas Eman. Simultaneouss iterative methods forsplit equality problem. Trans Math Prog Appl, 2013, 1:1-11
[13] Moudafi A. Split monotone variational inclusions. J Optim Theory Appl, 2011, 150:275-283
[14] Takahashi W. Iterative methods for split feasibility problems and split common null point problems in Banach spaces//The 9th International Conference on Nonlinear Analysis and Convex Analysis. Thailand, Jan:Chiang Rai, 2015:21-25
[15] Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Stud, 1994, 63:123-145
[16] Censor Y, Segal A. The split common fixed point problem for directed operators. J Convex Analysis, 2009, 16:587-600
[17] Eslamian M, Latif A. General split feasibility problems in Hilbert spaces. Abst Appl Anal, 2013, 2013:Article ID 805104
[18] Chen R D, Wang J, Zhang H W. General split equality problems in Hilbert spaces. Fixed Point Theory Appl, 2014, 2014:35
[19] Chuang C S. Strong convergence theorems for the split variational inclusion problem in Hilbert spaces. Fixed Point Theory Appl, 2013, 2013:350
[20] Chang S S, Wang L. Strong convergence theorems for the general split variational inclusion problem in Hilbert spaces. Fixed Point Theory Appl, 2014, 2014:171
[21] Chang S S, Agarwal Ravi P. Strong convergence theorems of general split equality problems for quasinonexpansive mappings. J Ineq Appl, 2014, 2014:367
[22] Chang S S, Wang L, Tang Y K, Wang G. Moudafi's open question and simultaneous iterative algorithm for general split equality variational inclusion problems and general split equality optimization problems. Fixed Point Theory Appl, 2014, 2014:215
[23] Naraghirad E. On an open question of Moudafi for convex feasibility problem in Hilbert spaces. Taiwan J Math, 2014, 18(2):371-408
[24] Tang J F, Chang S S, Liu M. General split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. Acta Math Sci, 2016, 36B(2):602-613

STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES

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