A new self-adaptive method for the split equality common fixed-point problem of quasi-nonexpansive mappings

References

• Moudafi A. Alternating CQ-algorithm for convex feasibility and split fixed-point problems. J Nonlinear Convex Anal. 2014;15:809–818.
   Web of Science ®Google Scholar
• Attouch H, Bolte J, Redont P, et al. Alternating proximal algorithms for weakly coupled minimization problems. Applications to dynamical games and PDEs. J Convex Anal. 2008;15:485–506.
   Web of Science ®Google Scholar
• Censor Y, Bortfeld T, Martin B, et al. A unified approach for inversion problems in intensity-modulated radiation therapy. Phys Med Biol. 2006;51:2353–2365. doi: 10.1088/0031-9155/51/10/001
   PubMed Web of Science ®Google Scholar
• Censor Y, Segal A. The split common fixed point problem for directed operators. J Convex Anal. 2009;16:587–600.
   Web of Science ®Google Scholar
• Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algor. 1994;8:221–239. doi: 10.1007/BF02142692
   Google Scholar
• Byrne C. Iterative oblique projection onto convex subsets and the split feasibility problem. Inverse Probl. 2002;18:441–453. doi: 10.1088/0266-5611/18/2/310
   Web of Science ®Google Scholar
• Cegielski A. General method for solving the split common fixed point problem. J Optim Theory Appl. 2015;165:385–404. doi: 10.1007/s10957-014-0662-z
   Web of Science ®Google Scholar
• Chang SS, Kim JK, Cho YJ, et al. Weak and strong convergence theorems of solutions to split feasibility problem for nonspreading type mapping in Hilbert spaces. Fixed Point Theory Appl. 2014;2014:11. doi: 10.1186/1687-1812-2014-11
   Google Scholar
• Dong QL, Tang YC, Cho YJ, et al. “Optimal” choice of the step length of the projection and contraction methods for solving the split feasibility problem. J Glob Optim. 2018;71:341–360. doi: 10.1007/s10898-018-0628-z
   Web of Science ®Google Scholar
• He S, Tian H, Xu HK. The selective projection method for convex feasibility and split feasibility problems. J Nonlinear Convex Anal. 2018;19(7):1199–1215.
   Web of Science ®Google Scholar
• Masad E, Reich S. A note on the multiple-set split convex feasibility problem in Hilbert space. J Nonlinear Convex Anal. 2007;8(3):367–371.
   Web of Science ®Google Scholar
• Moudafi A. A note on the split common fixed-point problem for quasi-nonexpansive operators. Nonlinear Anal. 2011;74:4083–4087. doi: 10.1016/j.na.2011.03.041
   Web of Science ®Google Scholar
• Qin X, Yao JC. A viscosity iterative method for a split feasibility problem. J Nonlinear Convex Anal. 2019;20:1497–1506.
   Web of Science ®Google Scholar
• Qin X, Petrusel A, Yao JC. CQ iterative algorithms for fixed points of nonexpansive mappings and split feasibility problems in Hilbert spaces. J Nonlinear Convex Anal. 2018;19:157–165.
   Web of Science ®Google Scholar
• Tang YC, Liu LW. Several iterative algorithms for solving the split common fixed point problem of directed operators with applications. Optimization. 2016;65(1):53–65. doi: 10.1080/02331934.2014.984708
   Web of Science ®Google Scholar
• Xu HK. A variable Krasnosel'skiĭ-Mann algorithm and the multiple-set split feasibility problem. Inverse Probl. 2006;22:2021–2034. doi: 10.1088/0266-5611/22/6/007
   Web of Science ®Google Scholar
• Xu HK. Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Probl. 2010;26: 105018, 17 pages. doi: 10.1088/0266-5611/26/10/105018
   Web of Science ®Google Scholar
• Yao Y, Liou YC, Postolache M. Self-adaptive algorithms for the split problem of the demicontractive operators. Optimization. 2018;67(9):1309–1319. doi: 10.1080/02331934.2017.1390747
   Web of Science ®Google Scholar
• Qu B, Xiu N. A note on the CQ algorithm for the split feasibility problem. Inverse Probl. 2005;21:1655–1665. doi: 10.1088/0266-5611/21/5/009
   Web of Science ®Google Scholar
• Wang F. On the convergence of CQ algorithm with variable steps for the split equality prblem. Numer Algor. 2017;74:927–935. doi: 10.1007/s11075-016-0177-9
   Web of Science ®Google Scholar
• Wang F. A new method for split common fixed-point problem without priori knowledge of operator norms. J Fixed Point Theory Appl. 2017;19:2427–2436. doi: 10.1007/s11784-017-0434-0
   Web of Science ®Google Scholar
• Yang Q. On variable-step relaxed projection algorithm for variational inequalities. J Math Anal Appl. 2005;302:166–179. doi: 10.1016/j.jmaa.2004.07.048
   Web of Science ®Google Scholar
• Yao Y, Yao Z, Abdou AA, et al. Self-adaptive algorithms for proximal split feasibility problems and strong convergence analysis. Fixed Point Theory Appl. 2015;2015:205. doi: 10.1186/s13663-015-0462-7
   Google Scholar
• Zhou H, Wang P. Adaptively relaxed algorithms for solving the split feasibility problem with a new step size. J Inequal Appl. 2014;2014:448. doi: 10.1186/1029-242X-2014-448
   Google Scholar
• López G, Martín-Márquez V, Wang F, et al. Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 2012;27:085004.
   Web of Science ®Google Scholar
• Chen P, Huang J, Zhang X. A primal-dual fixed-point algorithm for convex separable minimization with applications to image restoration. Inverse Probl. 2013;29: 025011(33pp).
   Web of Science ®Google Scholar
• Zhao J, Hou D. A self-adaptive iterative algorithm for the split common fixed point problems. Numer Algor. 2019;82:1047–1063. doi: 10.1007/s11075-018-0640-x
   Web of Science ®Google Scholar
• Moudafi A, Al-Shemas E. Simultaneous iterative methods for split equality problems and application. Trans Math Program Appl. 2013;1:1–11.
   Google Scholar
• Zhao J. Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms. Optimization. 2015;64(12):2619–2630. doi: 10.1080/02331934.2014.883515
   Web of Science ®Google Scholar
• Byrne C, Moudafi A. Extensions of the CQ algorithms for the split feasibility and split equality problems. Documents De Travail. 2013;18(8):1485–1496.
   Google Scholar
• Cui H, Ceng L, Wang F. Weak convergence theorems on the split common fixed point problem for demicontractive continuous mappings. J Funct Spaces. 2018;2018: 9610257, 7 pp.
   Web of Science ®Google Scholar
• Eslamian M, Shehu Y, Iyiola OS. A strong convergence theorem for a general split equality problem with applications to optimization and equilibrium problem. Calcolo. 2018;55:48. Available from: https://doi.org/10.1007/s10092-018-0290-3.
   Web of Science ®Google Scholar
• Giang DM, Strodiot JJ, Nguyen VH. Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space. RACSAM Rev R Acad Cienc Exactas Fis Nat Ser A Mat. 2017;111:983–998. doi: 10.1007/s13398-016-0338-7
   Web of Science ®Google Scholar
• Wang Y, Kim TH, Fang X. Weak and strong convergence theorems for the multiple-set split equality common fixed-point problems of demicontractive mappings. J Funct Spaces. 2017;2017: 5306802, 11 pp.
   Web of Science ®Google Scholar
• Wang Y, Kim TH, Chen R, et al. The multiple-set split equality common fixed point problems for demicontractive mappings without prior knowledge of operator norms. J Nonlinear Convex Anal. 2017;18(10):1849–1865.
   Web of Science ®Google Scholar
• Zhao J, He S. Viscosity approximation methods for split common fixed-point problem of directed operators. Numer Funct Anal Optim. 2015;36(4):528–547. doi: 10.1080/01630563.2015.1015079
   Web of Science ®Google Scholar
• Zhao J, Jia Y, Zhang H. General alternative regularization methods for split equality common fixed-point problem. Optimization. 2018;67(5):619–635. doi: 10.1080/02331934.2017.1412437
   Web of Science ®Google Scholar
• Zhao J, Wang S. Viscosity approximation methods for the split equality common fixed point problem of quasi-nonexpansive operators. Acta Math Sci Ser B Engl Ed. 2016;36(5):1474–1486. doi: 10.1016/S0252-9602(16)30083-2
   Web of Science ®Google Scholar
• Che H, Chen H, Li M. A new simultaneous iterative method with a parameter for solving the extended split equality problem and the extended split equality fixed point problem. Numer Algor. 2018;79:1231–1256. Available from: https://doi.org/10.1007/s11075-018-0482-6.
   Web of Science ®Google Scholar
• Zegeye H. The general split equality problem for Bregman quasi-nonexpansive mappings in Banach spaces. J Fixed Point Theory Appl. 2018;20:6. doi: 10.1007/s11784-018-0482-0
   Web of Science ®Google Scholar
• Chidume CE, Romanus OM, Nnyaba UV. An iterative algorithm for solving split equality fixed point problems for a class of nonexpansive-type mappings in Banach spaces. Numer Algor. 2019;82:987–1007. Available from: https://doi.org/10.1007/s11075-018-0638-4.
   Web of Science ®Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York: Springer; 2011. (CMS books in mathematics).
   Google Scholar