Acta mathematica scientia, Series B >
STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES
Received date: 2015-07-17
Revised date: 2016-04-18
Online published: 2016-12-25
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.
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.
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 . DOI: 10.1016/S0252-9602(16)30096-0
[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
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