This work proposes a novel method for solving the general split common fixed point problem of demicontractive operators in the framework of real Hilbert spaces. Our proposed technique is principally based on the Mann algorithm. The proof of the weak convergence theorem is additionally established under some particular conditions. We subsequently verify the convergence of our algorithm via numerical examples.
[1] H.H. Bauschke, J.M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev. 38 (1996)
367-426.
[2] H.H. Bauschke, P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in
Mathematics, Springer, New York (2011).
[3] C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl. 18 (2002) 441-453.
[4] Y. Censor, A. Segal, The split common ?xed point problem for directed operators, J. Convex Anal. 16(2) (2009) 587-600.
[5] Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms.
8(2) (1994) 221-239.
[6] W. Chaolamjiak, S.A. Khan, H.A. Hammad, H. Dutta, Weak and strong convergence results for the modified Noor iteration
of three quasi-nonexpansive multivalued mappings in Hilbert spaces, Filomat. 34(8) (2020) 2495-2510.
[7] T.L. Hicks, J.D. Kubicek, On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl. 59 (1977) 498-504.
[8] A. Kangtunyakarn, Iterative scheme for finding solutions of the general split feasibility problem and the general constrained
minimization problems, Filomat. 33(1) (2019) 233-243.
[9] S. Kesornporm, N. Pholasa, P. Cholamjiak, On the convergenece analysis of the gradient-CQ algorithms for the split
feasibility problem, Numer. Algorithms. 84(3) (2020) 997-1017.
[10] S. Maruster, The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Am. Math. Soc. 63 (1977) 69-73.
[11] A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Probl. 26(5) (2010) 055007.
[12] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math.
Soc. 73 (1967) 595-597.
[13] S. Suantai, W. Cholamjiak, P. Cholamjiak, An implicit iteration process for a finite family of multi-valued mappings in
Banach spaces, Appl. Math. Lett. 25 (2012) 1656-?1660.
[14] S. Suantai, K. Kankam, P. Cholamjiak, W. Cholamjiak, A parallel monotone hybrid algorithm for a finite family of
G−nonexpansive mappings in Hilbert spaces endowed with a graph applicable in signal recovery, Comp. Appl. Math. 40
(2021) 145.
[15] R. Suparatulatorn, S. Suantai, N. Phudolsitthiphat, Reckoning solution of split common fixed point problems by using
inertial self-adaptive algorithms, RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 113 (2019) 3101-3114.
[16] X.X. Zheng, Y. Yao, Y.C. Liou, L.M. Leng, Fixed point algorithms for the split problem of demicontractive operators, J.
Nonlinear Sci. Appl. 10 (2017) 1263-1269.
Year 2022,
Volume: 5 Issue: 3, 213 - 221, 30.09.2022
[1] H.H. Bauschke, J.M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev. 38 (1996)
367-426.
[2] H.H. Bauschke, P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in
Mathematics, Springer, New York (2011).
[3] C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Probl. 18 (2002) 441-453.
[4] Y. Censor, A. Segal, The split common ?xed point problem for directed operators, J. Convex Anal. 16(2) (2009) 587-600.
[5] Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms.
8(2) (1994) 221-239.
[6] W. Chaolamjiak, S.A. Khan, H.A. Hammad, H. Dutta, Weak and strong convergence results for the modified Noor iteration
of three quasi-nonexpansive multivalued mappings in Hilbert spaces, Filomat. 34(8) (2020) 2495-2510.
[7] T.L. Hicks, J.D. Kubicek, On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl. 59 (1977) 498-504.
[8] A. Kangtunyakarn, Iterative scheme for finding solutions of the general split feasibility problem and the general constrained
minimization problems, Filomat. 33(1) (2019) 233-243.
[9] S. Kesornporm, N. Pholasa, P. Cholamjiak, On the convergenece analysis of the gradient-CQ algorithms for the split
feasibility problem, Numer. Algorithms. 84(3) (2020) 997-1017.
[10] S. Maruster, The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Am. Math. Soc. 63 (1977) 69-73.
[11] A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Probl. 26(5) (2010) 055007.
[12] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math.
Soc. 73 (1967) 595-597.
[13] S. Suantai, W. Cholamjiak, P. Cholamjiak, An implicit iteration process for a finite family of multi-valued mappings in
Banach spaces, Appl. Math. Lett. 25 (2012) 1656-?1660.
[14] S. Suantai, K. Kankam, P. Cholamjiak, W. Cholamjiak, A parallel monotone hybrid algorithm for a finite family of
G−nonexpansive mappings in Hilbert spaces endowed with a graph applicable in signal recovery, Comp. Appl. Math. 40
(2021) 145.
[15] R. Suparatulatorn, S. Suantai, N. Phudolsitthiphat, Reckoning solution of split common fixed point problems by using
inertial self-adaptive algorithms, RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 113 (2019) 3101-3114.
[16] X.X. Zheng, Y. Yao, Y.C. Liou, L.M. Leng, Fixed point algorithms for the split problem of demicontractive operators, J.
Nonlinear Sci. Appl. 10 (2017) 1263-1269.
Charoensawan, P., & Suparatulatorn, R. (2022). A modified Mann algorithm for the general split problem of demicontractive operators. Results in Nonlinear Analysis, 5(3), 213-221. https://doi.org/10.53006/rna.1034213
AMA
Charoensawan P, Suparatulatorn R. A modified Mann algorithm for the general split problem of demicontractive operators. RNA. September 2022;5(3):213-221. doi:10.53006/rna.1034213
Chicago
Charoensawan, Phakdi, and Raweerote Suparatulatorn. “A Modified Mann Algorithm for the General Split Problem of Demicontractive Operators”. Results in Nonlinear Analysis 5, no. 3 (September 2022): 213-21. https://doi.org/10.53006/rna.1034213.
EndNote
Charoensawan P, Suparatulatorn R (September 1, 2022) A modified Mann algorithm for the general split problem of demicontractive operators. Results in Nonlinear Analysis 5 3 213–221.
IEEE
P. Charoensawan and R. Suparatulatorn, “A modified Mann algorithm for the general split problem of demicontractive operators”, RNA, vol. 5, no. 3, pp. 213–221, 2022, doi: 10.53006/rna.1034213.
ISNAD
Charoensawan, Phakdi - Suparatulatorn, Raweerote. “A Modified Mann Algorithm for the General Split Problem of Demicontractive Operators”. Results in Nonlinear Analysis 5/3 (September 2022), 213-221. https://doi.org/10.53006/rna.1034213.
JAMA
Charoensawan P, Suparatulatorn R. A modified Mann algorithm for the general split problem of demicontractive operators. RNA. 2022;5:213–221.
MLA
Charoensawan, Phakdi and Raweerote Suparatulatorn. “A Modified Mann Algorithm for the General Split Problem of Demicontractive Operators”. Results in Nonlinear Analysis, vol. 5, no. 3, 2022, pp. 213-21, doi:10.53006/rna.1034213.
Vancouver
Charoensawan P, Suparatulatorn R. A modified Mann algorithm for the general split problem of demicontractive operators. RNA. 2022;5(3):213-21.