Strong convergence theorems for a solution of split common fixed point problem involving \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings in Banach spaces
Volume 30, Issue 2, pp 173--189
https://doi.org/10.22436/jmcs.030.02.08
Publication Date: December 25, 2022
Submission Date: September 27, 2022
Revision Date: November 07, 2022
Accteptance Date: November 29, 2022
Authors
D. Jenber
- Department of Mathematics , Bahir Dar University, Bahir Dar, Ethiopia.
- Department of Mathematics, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia.
H. Zegeye
- Department of Mathematics , Botswana International University of Science and Technology, Private Bag 16, Palapye, Botswana.
M. H. Takele
- Department of Mathematics, Bahir Dar University, Bahir Dar, Ethiopia.
A. R. Tufa
- Department of Mathematics , University of Botswana, Private Bag 00704 Gaborone, Botswana.
Abstract
The purpose of this paper is to propose a method for approximating the solution of the split common fixed point problem involving \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings in the setting of two Banach spaces using \(G_f(.,.)\) functional.
We prove that the proposed method converges strongly to a solution of the split common fixed point problem. In addition, we provide some applications of our method and provide numerical results to demonstrate the applicability
of the proposed method.
Share and Cite
ISRP Style
D. Jenber, H. Zegeye, M. H. Takele, A. R. Tufa, Strong convergence theorems for a solution of split common fixed point problem involving \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings in Banach spaces, Journal of Mathematics and Computer Science, 30 (2023), no. 2, 173--189
AMA Style
Jenber D., Zegeye H., Takele M. H., Tufa A. R., Strong convergence theorems for a solution of split common fixed point problem involving \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings in Banach spaces. J Math Comput SCI-JM. (2023); 30(2):173--189
Chicago/Turabian Style
Jenber, D., Zegeye, H., Takele, M. H., Tufa, A. R.. "Strong convergence theorems for a solution of split common fixed point problem involving \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings in Banach spaces." Journal of Mathematics and Computer Science, 30, no. 2 (2023): 173--189
Keywords
- Split common fixed point problem
- \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings
- Banach space
MSC
References
-
[1]
Y. I. Alber, Generalized projection operators in Banach spaces: properties and applications, Funct. Differential Equations Israel Sem., 1993 (1993), 1–21
-
[2]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: Properties and applications, In: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, 1996 (1996), 15–50
-
[3]
E. Bonacker, A. Gibali, K.-H. K¨ ufer, Nesterov perturbations and projection methods applied to IMRT, Nonlinear Var. Anal., 4 (2020), 63–86
-
[4]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441–453
-
[5]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2003), 103–120
-
[6]
C. L. Byrne, Y. Censor, A. Gibali, S. Reich, Weak and strong convergence of algorithms for the split common null point problem, J. Nonlinear Convex Anal., 13 (2012), 759–775
-
[7]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Physics in Medicine & Biology, 51 (2006), 12 pages
-
[8]
Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221–239
-
[9]
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
-
[10]
Y. Censor, A. Gibali, S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms, 59 (2012), 301–323
-
[11]
Y. Censor, A. Motova, A. Segal, Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, J. Math. Anal. Appl., 327 (2007), 1244–1256
-
[12]
Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587–600
-
[13]
J.-Z. Chen, H.-Y. Hu, L.-C. Ceng, Strong convergence of hybrid Bregman projection algorithm for split feasibility and fixed point problems in Banach spaces, J. Nonlinear Sci. Appl., 10 (2017), 192–204
-
[14]
I. Cioranescu, Geometry of Banach spaces, duality mappings and nonlinear problems, Springer Science & Business Media, Berlin (2012)
-
[15]
J. Garcia-Falset, O. Muniz-Perez, S. Reich, Domains of accretive operators in Banach spaces, Proc. Roy. Soc. Edinburgh Sect. A, 146 (2016), 325–336
-
[16]
F. Kohsaka, W. Takahashi, Existence and approximation of fixed points of firmly nonexpansive type mappings in Banach spaces, SIAM J. Optim., 19 (2008), 824–835
-
[17]
J. L. Li, The generalized projection operator on reflexive Banach spaces and its applications, J. Math. Anal. Appl., 306 (2005), 55–71
-
[18]
X. Li, N.-J. Huang, D. O’Regan, Strong convergence theorems for relatively nonexpansive mappings in Banach spaces with applications, Comput. Math. Appl., 60 (2010), 1322–1331
-
[19]
X. Liu, Z. Chen, J. Liu, On the split common fixed point problem for strict quasi- -pseudocontractive mappings in Banach spaces, Numerical Algorithms, 87 (2021), 1129–1145
-
[20]
G. L´opez, V. Martin-M´arquez, F. Wang, H.-K. Xu, Solving the split feasibility problem without prior knowledge of matrix norms, Inverse Problems, 28 (2012), 18 pages
