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Articles

New algorithms for the split common null point problem

Pages 1141-1160 | Received 17 Jun 2019, Accepted 05 Jun 2020, Published online: 23 Jun 2020

References

  • Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in product space. Numer Algorithms. 1994;8:221–239. doi: 10.1007/BF02142692
  • 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
  • Censor Y, Elfving T, Kopf N, et al. The multiple-sets split feasibility problem and its applications for inverse problems. Inverse Probl. 2005;21:2071–2084. doi: 10.1088/0266-5611/21/6/017
  • Deepho J, Thounthong P, Kumam P, et al. A new general iterative scheme for split variational inclusion and fixed point problems of k-strict pseudo-contraction mappings with convergence analysis. J Comput Appl Math. 2017;318:293–306. doi: 10.1016/j.cam.2016.09.009
  • Ceng LC, Ansari QH, Yao JC. An extragradient method for solving split feasibility and fixed point problems. Comput Math Apll. 2012;64:633–642. doi: 10.1016/j.camwa.2011.12.074
  • Xu HK. Iterative methods for the split feasibilty problem in infinite-dimensional Hilbert spaces. Inverse Probl. 2010;26: 105018. Article ID 105018. doi: 10.1088/0266-5611/26/10/105018
  • Shehu Y, Iyiola OS. Convergence analysis for the proximal split feasibiliy problem using an inertial extrapolation term method. J Fixed Point Theory Appl. 2017;19:2483–2510. doi: 10.1007/s11784-017-0435-z
  • Combettes PL. The convex feasible problem in image recovery. In: Hawkes P, editor. Advance in image and electronphysics. New York: Academic Press, 95; 1996. p. 155–270.
  • Censor Y, Gibali A, Reich S. Algorithms for the split variational inequality problem. Numer Algorithms. 2012;59:301–323. doi: 10.1007/s11075-011-9490-5
  • Gibali A. A new split inverse problem and application to least intensity feasible solutions. Pure Appl Funct Anal. 2017;2(2):243–258.
  • Moudafi A. Split monotone variational inclusions. J Optim Theory Appl. 2011;150:275–283. doi: 10.1007/s10957-011-9814-6
  • Byrne C, Censor Y, Gibali A, et al. Weak and strong convergence of algorithms for the split common null point problem. J. Nonlinear Convex Anal. 2012;13:759–775.
  • Byrne C. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 2002;18:441–453. doi: 10.1088/0266-5611/18/2/310
  • Moudafi A, Thakur BS. Solving proximal split feasibilty problem without prior knowledge of matrix norms. Optim Lett. 2013;8(7):00–00. DOI 10.1007/s11590-013-0708-4.
  • Gibali A, Mai DT, Nguyen TV. A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications. J Indus Manag Optim. 2018;2018:1–25.
  • Sitthithakerngkiet K, Deepho J, Martinez-Moreno J, et al. Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems. Numer Algorithms. 2018. Doi:10.1007/s11075-017-0462-2
  • Kazmi KR, Rizvi SH. An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping. Optim Lett. 2014;8:1113–1124. doi: 10.1007/s11590-013-0629-2
  • Promluang K, Kumam P. Viscosity approximation method for split common null point problems between Banach spaces and Hilbert spaces. J Inform Math Sci. 2017;9(1):27–44.
  • Suantai S, Srisap K, Naprang N, et al. Convergence theorems for finding the split common null point in Banach spaces.Appl. Gen Topol. 2017;18(2):3345–360.
  • Ealamian M, Zamani G, Raeisi M. Split common null point and common fixed point problems between Banach spaces and Hilbert spaces. Mediterr J Math. 2017;14(119):
  • Chidume CE, Romanus OM, Nnyaba UV. A new iterative algorithm for zeros of generalized Phi-strongly monotone and bounded maps with application. Brit J Math Comput Sci. 2016;18(1):1–14. Article no. BJMCS. 25884. doi: 10.9734/BJMCS/2016/25884
  • Chidume CE. Geometric properties of Banach spaces and nonlinear iterations. London: Springer; 2009. (Lectures Notes in Mathematics; 1965).
  • López G, Martin-Marquez V, Xu HK. Solving the split feasibilty problem without prior knowledge of matrix norms. Inverse Probl. 2012;28: ID085004 doi: 10.1088/0266-5611/28/8/085004
  • Tang Y, Gibali A. New self-adaptive step size algorithms for solving split variational inclusion problems and its applications. Numer Algorithms. 2019. doi:10.1007/s11075-019-00683-0
  • Xu HK. Iterative algorithms for nonliear operators. J Lond Math Soc. 2002;66(2):240–256. doi: 10.1112/S0024610702003332
  • Maingé PE. Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces. J Math Anal Appl. 2007;325:469–479. doi: 10.1016/j.jmaa.2005.12.066
  • Opial Z. Weak convergence of the sequence of successive approximations for nonexpansivemappings. Bull Am Math Soc. 1967;73:591–598. doi: 10.1090/S0002-9904-1967-11761-0
  • Maingé PE. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-valued Anal. 2008;16:899–912. doi: 10.1007/s11228-008-0102-z
  • Censor Y, Segal A. The split common fixed point problem for directed operators. J Convex Anal. 2009;16:587–600.
  • Moudafi A. Split monotone variational inclusions. J Optim Theory Appl. 2011;150:275–283. doi: 10.1007/s10957-011-9814-6

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