216
Views
4
CrossRef citations to date
0
Altmetric
Articles

The Split Equality Fixed Point Problem for Quasi-Pseudo-Contractive Mappings Without Prior Knowledge of Norms

&
Pages 759-777 | Received 23 Sep 2019, Accepted 28 Sep 2019, Published online: 12 Oct 2019

References

  • Moudafi, A. (2011). Split monotone variational inclusions. J. Optim. Theory Appl. 150(2):275–283. DOI: 10.1007/s10957-011-9814-6.
  • Moudafi, A. (2013). A relaxed alternating CQ algorithm for convex feasibility problems. Nonlinear Anal. 79:117–121. DOI: 10.1016/j.na.2012.11.013.
  • Moudafi, A., Al-Shemas, E. (2013). Simultaneous iterative methods for split equality problem. Trans. Math. Program. Appl. 1:1–11.
  • Aleyner, A., Reich, S. (2008). Block iterative algorithms for solving convex feasibility problem in hilbert and banach spaces. J. Math. Anal. Appl. 343(1):427–435. DOI: 10.1016/j.jmaa.2008.01.087.
  • Attouch, H., Bolte, J., Redonte, P., Soubeyran, A. (2008). Alternating proximal algorithms for weakly coupled minimization problems. Applications to dynamical games and PDEs. J. Convex Anal. 15:485–506.
  • Bauschke, H. H., Borwein, J. M. (1996). On the projection algorithms for solving convex feasibility problems. SIAM Rev. 38(3):367–426. DOI: 10.1137/S0036144593251710.
  • Masad, E., Reich, S. (2007). A note on the multiple-set split convex feasibility problem in Hilbert spaces. J. Nonlinear Convex Anal. 8:367–371.
  • Xu, H. K. (2010). Iterative methods for the split feasibility problem in infinite dimensional Hilbert spaces. Inverse Probl. 26:105018. DOI: 10.1088/0266-5611/26/10/105018.
  • Xu, H. K. (2006). A variable Krasnosel’skii-Mann algorithm and the multiple-set split feasibility problem. Inverse Probl. 22(6):2021–2034. DOI: 10.1088/0266-5611/22/6/007.
  • Yang, Q. (2004). The relaxed CQ algorithm for solving the split feasibility problem. Inverse Probl. 20(4):1261–1266. DOI: 10.1088/0266-5611/20/4/014.
  • Yao, Y., Chen, R., Marino, G., Liou, Y. C. (2012). Applications of fixed points and optimization methods to the multiple-sets split feasibility problem. J. Appl. Math. 2012:1. Article ID 927530. DOI: 10.1155/2012/927530.
  • Zhao, J., Yang, Q. (2005). Several solution methods for the split feasibility problem. Inverse Probl. 21(5):1791–1799. DOI: 10.1088/0266-5611/21/5/017.
  • Censor, Y., Elfving, T. (1994). A multiprojection algorithm using Bregman projections in a product space. Numer. Algor. 8(2):221–239. DOI: 10.1007/BF02142692.
  • Byrne, C. (2004). A unified treatment of iterative algorithms in signal processing and image reconstruction. Inverse Probl. 20(1):103–120. DOI: 10.1088/0266-5611/20/1/006.
  • Censor, Y., Bortfeld, T., Martin, B., Trofimov, A. (2006). A unified approach for inversion problems in intensity-modulated radiation therapy. Phys. Med. Biol. 51(10):2353–2365. DOI: 10.1088/0031-9155/51/10/001.
  • Censor, Y., Elfving, T., Kopf, N., Bortfeld, T. (2005). The multisets split feasibility problem and its applications to inverse problems. Inverse Probl. 21(6):2071–2084. DOI: 10.1088/0266-5611/21/6/017.
  • 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.
  • Censor, Y., Segal, A. (2009). The split common fixed point problem for directed operators. J. Convex Anal. 16:587–600.
  • Byrne, C., Censor, Y., Gibali, A., Reich, S. (2012). The split common null point problem. J. Nonlinear Convex Anal. 13:759–775.
  • Boikanyo, O. A. (2015). A strongly convergent algorithm for the split common fixed point problem. Appl. Math. Comput. 265:844–853. DOI: 10.1016/j.amc.2015.05.130.
  • Moudafi, A. (2014). Alternating CQ algorithm for convex feasibility and split fixed point problems. J. Nonlinear Convex Anal. 15:809–818.
  • Che, H., Li, M. (2015). A simultaneous iterative method for split equality problems of two finite families of strictly pseudononspreading mappings without prior knowledge of operator norms. Fixed Point Theory Appl. 2015:1. DOI: 10.1186/1687-1812-2015-1.
  • Zhao, J. (2015). Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms. Optimization 64(12):2619–2630. DOI: 10.1080/02331934.2014.883515.
  • Chang, S.-S., Wang, L., Qin, L. J. (2015). Split equality fixed point problem for quasi-pseudo-contractive mappings with applications. Fixed Point Theory Appl. 2015(1):208. DOI: 10.1186/s13663-015-0458-3.
  • Osilike, M. O., Igbokwe, D. I. (2000). Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations. Comput. Math. Appl. 40(4–5):559–567. DOI: 10.1016/S0898-1221(00)00179-6.
  • Zegeye, H., Shahzad, N. (2011). Convergence of mann’s type iteration method for generalized asymptotically nonexpansive mappings. Comput. Math. Appl. 62(11):4007–4014. DOI: 10.1016/j.camwa.2011.09.018.
  • Goebel, K., Reich, S. (1984). Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. New York: Marcel Dekker.
  • Takahashi, W. (2000). Nonlinear Functional Analysis. Yokahama, Japan: Yokohama Publishers.
  • Yao, Y., Liou, Y.-C., Yao, J.-C. (2015). Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction. Fixed Point Theory Appl. 2015(1):127. DOI: 10.1186/s13663-015-0376-4.
  • Xu, H. K. (2002). Iterative algorithms for nonlinear operators. J. London Math. Soc. 66(1):240–256. DOI: 10.1112/S0024610702003332.
  • Maingé, P. E. (2008). Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal. 16(7–8):899–912. DOI: 10.1007/s11228-008-0102-z.
  • Zhou, H. (2009). Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in banach spaces. Nonlinear Anal. 70(11):4039–4046. DOI: 10.1016/j.na.2008.08.012.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.