Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings
Volume 16, Issue 1, pp 1--17
http://dx.doi.org/10.22436/jnsa.016.01.01
Publication Date: March 10, 2023
Submission Date: October 10, 2022
Revision Date: February 14, 2023
Accteptance Date: February 22, 2023
Authors
C. Suanoom
- Program of Mathematics, Science and Applied Science center, Faculty of Science and Technology, Kamphaeng Phet Rajabhat, Kamphaeng Phet 62000, Thailand.
S. E. Yimer
- Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, Ethiopia.
A. G. Gebrie
- Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, Ethiopia.
Abstract
In this paper, two new inertial CQ-algorithms with strong convergence results are constructed to approximate the solution of the generalized split common fixed point problem: given as a task of finding a point that belongs to the intersection of an infinite family of fixed point sets of demimetric mappings such that its image under an infinite number of linear transformations belongs to the intersection of another infinite family of fixed point sets of demimetric mappings in the image space. The algorithms are established based on the CQ-projection method with inertial effect and step-size selection technique so that the implementation of the proposed algorithms does not need any prior information about the operator norms. The proposed methods improve, complement, and generalize many of the important results in the literature.
Share and Cite
ISRP Style
C. Suanoom, S. E. Yimer, A. G. Gebrie, Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings, Journal of Nonlinear Sciences and Applications, 16 (2023), no. 1, 1--17
AMA Style
Suanoom C., Yimer S. E., Gebrie A. G., Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings. J. Nonlinear Sci. Appl. (2023); 16(1):1--17
Chicago/Turabian Style
Suanoom, C., Yimer, S. E., Gebrie, A. G.. "Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings." Journal of Nonlinear Sciences and Applications, 16, no. 1 (2023): 1--17
Keywords
- Split common fixed-point problem
- \(\kappa\)-demimetric mapping
- inertial term
- CQ-algorithm
- Hilbert space
- strong convergence
MSC
References
-
[1]
A. Abkar, E. Shahrosvand, The split common fixed point problem of two infinite families of demicontractive mappings and the split common null point problem, Filomat, 31 (2017), 3859–3874
-
[2]
H. H. Bauschke, P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, Springer, New York (2011)
-
[3]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197–228
-
[4]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse probl., 20 (2004), 103–120
-
[5]
C. Byrne, Y. Censor, A. Gibali, S. Reich, The split common null point problem, J. Nonlinear Convex Anal., 13 (2012), 759–775
-
[6]
A. Cegielski, General method for solving the split common fixed point problem, J. Optim. Theory Appl., 165 (2015), 385–404
-
[7]
Y. Censor, W. Chen, P. L. Combettes, R. Davidi, G. T. Herman, On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints, Comput. Optim. Appl., 51 (2012), 1065–1088
-
[8]
Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse problems, 21 (2005), 2071–2084
-
[9]
Y. Censor, A. Gibali, S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms, 59 (2012), 301–323
-
[10]
Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587–600
-
[11]
S.-S. Chang, J. K. Kim, X. R. Wang, Modified block iterative algorithm for solving convex feasibility problems in Banach spaces, J. Inequal. Appl., 2010 (2010), 1–14
-
[12]
P. L. Combettes, S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6 (2005), 117–136
-
[13]
M. Eslamian, General algorithms for split common fixed point problem of demicontractive mappings, Optimization, 65 (2016), 443–465
-
[14]
A. G. Gebrie, A novel low-cost method for generalized split inverse problem of finite family of demimetric mappings, Comput. Appl. Math., 40 (2021), 1–18
-
[15]
A. G. Gebrie, Weak and strong convergence adaptive algorithms for generalized split common fixed point problems, Optimization, 71 (2022), 3711–3736
-
[16]
A. G. Gebrie, R.Wangkeeree, Proximal method of solving split system of minimization problem, J. Appl. Math. Comput., 63 (2020), 107–132
-
[17]
A. G. Gebrie, R. Wangkeeree, Parallel proximal method of solving split system of fixed point set constraint minimization problems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat., 114 (2020), 1–29
-
[18]
Z. He, The split equilibrium problem and its convergence algorithms, J. Inequal. Appl., 2012 (2012), 1–15
-
[19]
J. M. Hendrickx, A. Olshevsky, Matrix p-norms are NP-hard to approximate if p 6= 1, 2,1, SIAM J. Matrix Anal. Appl., 31 (2010), 2802–2812
-
[20]
T. L. Hicks, J. D. Kubicek, On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl., 59 (1977), 498–504
-
[21]
M. Hojo, W. Takahashi, Strong convergence theorems by hybrid methods for demimetric mappings in Banach spaces, J. Nonlinear Convex Anal., 17 (2016), 1333–1344
-
[22]
M. Hojo, W. Takahashi, I. Termwuttipong, Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces, Nonlinear Anal., 75 (2012), 2166–2176
-
[23]
H. Iiduka, Iterative algorithm for triple-hierarchical constrained nonconvex optimization problem and its application to network bandwidth allocation, SIAM J. Optim., 22 (2012), 862–878
-
[24]
H. Iiduka, Fixed point optimization algorithms for distributed optimization in networked systems, SIAM J. Optim., 23 (2013), 1–26
-
[25]
P. Kocourek, W. Takashi, J.-C. Yao, Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese J. Math., 14 (2010), 2497–2511
-
[26]
C. Martinez-Yanes, H.-K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Analysis: Theory, Methods & Applications, 64 (2006), 2400–2411
-
[27]
A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Probl., 26 (2010), 6 pages
-
[28]
A. Moudafi, A note on the split common fixed-point problem for quasi-nonexpansive operators, Nonlinear Anal., 74 (2011), 4083–4087
-
[29]
A. Moudafi, M. Th´era, Proximal and dynamical approaches to equilibrium problems, Ill-posed variational problems and regularization techniques (Trier, 1998), 477 (1999), 187–201
-
[30]
G. Marino, H.-K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl., 329 (2007), 336–346
-
[31]
B. T. Polyak, Some methods of speeding up the convergence of iteration methods, Ussr Comput. Math. Math. Phys., 4 (1964), 1–17
-
[32]
X. Qin, Y. J. Cho, S. M. Kang, An iterative method for an infinite family of nonexpansive mappings in Hilbert spaces, Bull. Malays. Math. Sci. Soc. (2), 32 (2009), 161–171
-
[33]
L.-J. Qin, G. Wang, Multiple-set split feasibility problems for a finite family of demicontractive mappings in Hilbert spaces, Math. Inequal. Appl., 16 (2013), 1151–1157
-
[34]
W. Takahashi, The split common fixed point problem and the shrinking projection method in Banach spaces, J. Convex Anal., 24 (2017), 1015–1028
-
[35]
S. Takahashi, W. Takahashi, The split common null point problem and the shrinking projection method in Banach spaces, Optimization, 65 (2016), 281–287
-
[36]
Y.-C. Tang, L.-W. Liu, Several iterative algorithms for solving the split common fixed point problem of directed operators with applications, Optimization, 65 (2016), 53–65
-
[37]
F. Wang, H.-K. Xu, Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal., 74 (2011), 4105– 4111
-
[38]
J. Zhaoa, Q. Yang, Several acceleration schemes for solving the multiple-sets split feasibility problem, Linear Algebra Appl., 473 (2012), 1648–1657
