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Research Article

Two Projection Methods for Solving the Split Common Fixed Point Problem with Multiple Output Sets in Hilbert Spaces

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Pages 973-988 | Received 12 May 2020, Accepted 09 Feb 2021, Published online: 14 Jun 2021

References

  • Censor, Y., Elfving, T. (1994). A multi projection algorithm using Bregman projections in a product space. Numer. Algor. 8(2):221–239. DOI: 10.1007/BF02142692.
  • Byrne, C. (2002). Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Prob. 18(2):441–453. DOI: 10.1088/0266-5611/18/2/310.
  • Byrne, C. (2004). A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Prob. 20(1):103–120. DOI: 10.1088/0266-5611/20/1/006.
  • Butnariu, D., Resmerita, E. (2006). Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces. Abstr. Appl. Anal. 2006:1–39. DOI: 10.1155/AAA/2006/84919.
  • Censor, Y., Elfving, T., Kopf, N., Bortfeld, T. (2005). The multiple-sets split feasibility problem and its application. Inverse Prob. 21(6):2071–2084. DOI: 10.1088/0266-5611/21/6/017.
  • Censor, Y., Gibali, A., Reich, S. (2012). Algorithms for the split variational inequality problems. Numer. Algor. 59(2):301–323. DOI: 10.1007/s11075-011-9490-5.
  • Dadashi, V. (2017). Shrinking projection algorithms for the split common null point problem. Bull. Aust. Math. Soc. 96(2):299–306. DOI: 10.1017/S000497271700017X.
  • Takahashi, S., Takahashi, W. (2016). The split common null point problem and the shrinking projection method in Banach spaces. Optimization. 65(2):281–287. DOI: 10.1080/02331934.2015.1020943.
  • Takahashi, W. (2015). The split feasibility problem and the shrinking projection method in Banach spaces. J. Nonlinear Convex Anal. 16:1449–1459.
  • Takahashi, W. (2015). The split common null point problem in Banach spaces. Arch. Math. 104(4):357–365. DOI: 10.1007/s00013-015-0738-5.
  • Wang, F., Xu, H.-K. (2011). Cyclic algorithms for split feasibility problems in Hilbert spaces. Nonlinear Anal. 74(12):4105–4111. DOI: 10.1016/j.na.2011.03.044.
  • Wang, S., Liu, X., An, Y.S. (2017). A new iterative algorithm for generalized split euilibrium problem in Hilbert spaces. Nonlinear Funct. Anal. Appl. 22:911–924.
  • Xu, H.-K. (2006). A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem. Inverse Prob. 22(6):2021–2034. DOI: 10.1088/0266-5611/22/6/007.
  • Xu, H.-K. (2010). Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Prob. 26(10):105018. DOI: 10.1088/0266-5611/26/10/105018.
  • Yang, Q. (2004). The relaxed CQ algorithm for solving the split feasibility problem. Inverse Prob. 20(4):1261–1266. DOI: 10.1088/0266-5611/20/4/014.
  • Zhang, C., Xu, Z. (2016). Hybrid steepest decent method for split variational inclusion and finite family of nonexpansive mappings. Nonlinear Funct. Anal. Appl. 21:399–412.
  • Masad, E., Reich, S. (2007). A note on the multiple-set split convex feasibility problem in Hilbert space. J. Nonlinear Convex Anal. 8:367–371.
  • Censor, Y., Segal, A. (2009). The split common fixed point problem for directed operators. J. Convex Anal. 16:587–600.
  • Moudafi, A. (2010). The split common fixed point problem for demicontractive mappings. Inverse Prob. 26(5):055007. DOI: 10.1088/0266-5611/26/5/055007.
  • Reich, S., Tuyen, T. M., Mai, T. N. H. (2020). The split feasibility problem with multiple output sets in Hilbert spaces. Optim. Lett. 14:2335–2353. DOI: 10.1007/s11590-020-01555-6.
  • Reich, S., Tuyen, T. M., Trang, N. M. (2019). Parallel iterative methods for solving the split common fixed point problem in Hilbert spaces. Numerical Funct. Anal. Optim. 41(7):778–805. DOI: 10.1080/01630563.2019.1681000.
  • Yang, L., Zhao, F., Kim, J.K. (2017). The split common fixed point problem for demicontractive mappings in Banach spaces. J. Comput. Anal. Appl. 22:858–873.
  • Zhao, J., Wang, S. (2015). Viscosity approximation method for the split common fixed point problem of quasi-strict pseudo-contractions without prior knowledge of operator norms. Nonlinear Funct. Anal. Appl. 20:199–213.
  • Kim, J. K., Salahuddin, Lim, W. H. (2017). General nonconvex split variational inequality problems. Korean J. Math. 25:469–481.
  • Byrne, C., Censor, Y., Gibali, A., Reich, S. (2012). The split common null point problem. J. Nonlinear Convex Anal. 13:759–775.
  • Kim, J. K., Tuyen, T. M. (2019). Parallel iterative method for solving the split common null point problem in Banach spaces. J. Nonlinear Convex Anal. 20:2075–2093.
  • Reich, S., Tuyen, T. M. (2020). Iterative methods for solving the generalized split common null point problem in Hilbert spaces. Optimization 69(5):1013–1038. DOI: 10.1080/02331934.2019.1655562.
  • Reich, S., Tuyen, T. M. (2020). Two projection methods for solving the multiple-set split common null point problem in Hilbert spaces. Optimization 69(9):1913–1934. DOI: 10.1080/02331934.2019.1686633.
  • Reich, S., Tuyen, T. M. (2020). A new algorithm for solving the split common null point problem in Hilbert spaces. Numer. Algor. 83(2):789–805. DOI: 10.1007/s11075-019-00703-z.
  • Tuyen, T. M., Thuy, N. T. T., Trang, N. M. (2019). A strong convergence theorem for a parallel iterative method for solving the split common null point problem in Hilbert spaces. J. Optim. Theory Appl. 183(1):271–291. DOI: 10.1007/s10957-019-01523-w.
  • Tuyen, T. M. (2019). A strong convergence theorem for the split common null point problem in Banach spaces. Appl. Math. Optim. 79(1):207–227. DOI: 10.1007/s00245-017-9427-z.
  • Tuyen, T. M., Ha, N. S., Thuy, N. T. T. (2019). A shrinking projection method for solving the split common null point problem in Banach spaces. Numer. Algor. 81(3):813–832. DOI: 10.1007/s11075-018-0572-5.
  • Tuyen, T. M., Ha, N. S. (2018). A strong convergence theorem for solving the split feasibility and fixed point problems in Banach spaces. J. Fixed Point Theory Appl. 20(4):140. DOI: 10.1007/s11784-018-0622-6.
  • Landweber, L. (1951). An iterative formula for Fredholm integral equations of the first kind. Am. J. Math. 73(3):615–624. DOI: 10.2307/2372313.
  • Goebel, K., Reich, S. (1984). Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. New York: Marcel Dekker.
  • Agarwal, R. P., O’Regan, D., Sahu, D. R. (2009). Fixed Point Theory for Lipschitzian-Type Mappings with Applications. New York: Springer.
  • Goebel, K., Kirk, W. A. (1990). Topics in Metric Fixed Point Theory. Cambridge Studies in Advanced Mathematics 28. Cambridge, UK: Cambridge University Press.

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