Strong convergence of two regularized relaxed extragradient schemes for solving the split feasibility and fixed point problem with multiple output sets

References

• Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms. 1994;8(2):221–239.
   Google Scholar
• Censor Y, Elfving T, Kopf N, et al. The multiple-sets split feasibility problem and its applications for inverse problems. Inverse Probl. 2005;21(6):2071–2084.
   Web of Science ®Google Scholar
• Byrne C. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 2004;20:103–120.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Algorithms for the split variational inequality problems. Numer Algorithms. 2012;59:301–323.
   Web of Science ®Google Scholar
• Dadashi V. Shrinking projection algorithms for the split common null point problem. Bull Aust Math Soc. 2017;96(2):299–306.
   Web of Science ®Google Scholar
• Takahashi W. The split feasibility problem and the shrinking projection method in Banach spaces. J Nonlinear Convex Anal. 2015;16(7):1449–1459.
   Web of Science ®Google Scholar
• Wang F, Xu H-K. Cyclic algorithms for split feasibility problems in Hilbert spaces. Nonlinear Anal. 2011;74(12):4105–4111.
   Web of Science ®Google Scholar
• Xu H-K. A variable Krasnosel'skii–Mann algorithm and the multiple-set split feasibility problem. Inverse Probl. 2006;22(6):2021–2034.
   Web of Science ®Google Scholar
• Xu H-K. Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Inverse Probl. 2010;26(10):Article ID 105018.
   Web of Science ®Google Scholar
• Byrne C. Iterative oblique projection onto convex subsets and the split feasibility problem. Inverse Probl. 2002;18(2):441–453.
   Web of Science ®Google Scholar
• Landweber L. An iterative formula for Fredholm integral equations of the first kind. Am J Math. 1951;73(3):615–624.
   Google Scholar
• Lu T, Zhao L, He H. A multi-view on the CQ algorithm for split feasibility problems: from optimization lens. J Appl Numer Optim. 2020;2:387–399.
   Google Scholar
• Moudafi A. Byrne's extended CQ-algorithms in the light of Moreau–Yosida regularization. Appl Set Valued Anal Optim. 2021;3:21–26.
   Google Scholar
• Xu H-K. Iterative algorithm for nonlinear operators. J Lond. Math Soc. 2002;66(1):240–256.
   Web of Science ®Google Scholar
• Censor Y, Segal A. The split common fixed point problem for directed operators. J Convex Anal. 2010;26(5):Article ID 055007.
   PubMedGoogle Scholar
• Cui H, Wang F. Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theory Appl. 2014;2014(1):1–8.
   Google Scholar
• Eslamian M, Eslamian P. Strong convergence of a split common fixed point problem. Numer Funct Anal Optim. 2016;37(10):1248–1266.
   Web of Science ®Google Scholar
• Shehu Y, Cholamjiak P. Another look at the split common fixed point problem for demicontractive operators. RACSAM. 2015;110(1):201–218.
   Google Scholar
• Taiwo A, Mewomo OT, Gibali A. A simple strong convergent method for solving split common fixed point problems. J Nonlinear Var Anal. 2021;5(5):777–793.
   Web of Science ®Google Scholar
• Ceng LC, Ansari QH, Yao JC. An extragradient methods for solving split feasibility and fixed point problems. Comput Math Appl. 2012;64(4):633–642.
   Web of Science ®Google Scholar
• Chen JZ, Ceng LC, Qiu YQ, et al. Extra-gradient methods for solving split feasibility and fixed point problems. Fixed Point Theory Appl. 2015;2015(1):1–21.
   Google Scholar
• Wongsasinchai P. SP-Type extragradient iterative methods for solving split feasibility and fixed point problems in Hilbert spaces. Int J Appl Math. 2021;51(2):1–7.
   Google Scholar
• Ceng L-C, Ansari QH, Yao JC. On relaxed viscosity iterative methods for variational inequalities in Banach spaces. J Comput Appl Math. 2009;230(2):813–822.
   Web of Science ®Google Scholar
• Ceng L-C, Ansari QH, Yao JC. Mann type iterative methods for finding a common solution of split feasibility and fixed point problems. Positivity. 2012;16(3):471–495.
   Web of Science ®Google Scholar
• Reich S, Taiwo A. A one-step Tikhonov regularization iterative scheme for solving split feasibility and fixed point problems. Minimax Theory Appl (Accepted for publication).
   Google Scholar
• Reich S, Truong MT, Mai TNH. The split feasibility problem with multiple output sets in Hilbert spaces. Optim Lett. 2020;14(8):2335–2353.
   Web of Science ®Google Scholar
• Okeke CC, Jolaoso LO, Shehu Y. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces. Int J Nonlinear Sci Numer Simul. 2021.
   Web of Science ®Google Scholar
• Zhang Y, Li Y. Two modified relaxed CQ-algorithms for the multiple-sets split feasibility problem. J Nonlinear Funct Anal. 2021;Article ID 39.
   Web of Science ®Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. Canada (LLC); CMS Books in Mathematics; 2011.
   Google Scholar
• Chidume CE. Geometric properties of Banach spaces and nonlinear iterations. London: Springer; 2009. (Lecture notes in mathematics 1965).
   Google Scholar
• Yamada I. The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. Inherently parallel algorithms in feasibility and optimization and their applications. Stud Comput Math. 2001;8:473–504.
   Google Scholar
• Zhou H. Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces. Nonlinear Anal Theory Methods Appl. 2009;70(11):4039–4046.
   Web of Science ®Google Scholar
• Taiwo A, Jolaoso LO, Mewomo OT. Viscosity approximation method for solving the multiple-set split equality common fixed point problems for quasi-pseudocontractive mappings in Hilbert spaces. J Ind Manag Optim. 2021;17(5):2733.
   Google Scholar
• Yao Y, Liou YC, Yao JC. Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction. Fixed Point Theory Appl. 2015;2015(1):1–19.
   Google Scholar
• Maingé PE. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set Valued Var Anal. 2008;16(7–8):899–912.
   Google Scholar
• Yao Y, Agarwal RP, Postolache M, et al. Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem. Fixed Point Theory Appl. 2014;2014(1):1–14.
   Google Scholar
• López G, Martín-Márquez V, Wang F, et al. Forward–backward splitting methods for accretive operators in Banach spaces. Abstr Appl Anal. 2012;2012:1–25.
   Google Scholar
• Cegielski A. Iterative methods for fixed point problems in Hilbert spaces. Berlin: Springer; 2012. (Lecture notes in mathematics; vol. 2057).
   Google Scholar
• Iyiola OS, Shehu Y. Convergence results of two-step inertial proximal point algorithm. Appl Numer Math. 2022;182:57–75.
   Web of Science ®Google Scholar