Strong-weak convergence of two algorithms for total asymptotically nonexpansive mappings
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Authors
Yan Hao
- School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, China.
- Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan 316022, China.
Chaoping Wang
- School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, China.
- Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan 316022, China.
Jie Zhou
- School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, China.
- Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan 316022, China.
Abstract
The purpose of this article is to investigate fixed point problems of total asymptotically nonexpansive mappings via two
different iterative algorithms. We obtain strong and convergence theorems in the framework of Hilbert spaces. The main results
improve and extend the recent corresponding results.
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ISRP Style
Yan Hao, Chaoping Wang, Jie Zhou, Strong-weak convergence of two algorithms for total asymptotically nonexpansive mappings, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2700--2709
AMA Style
Hao Yan, Wang Chaoping, Zhou Jie, Strong-weak convergence of two algorithms for total asymptotically nonexpansive mappings. J. Nonlinear Sci. Appl. (2017); 10(5):2700--2709
Chicago/Turabian Style
Hao, Yan, Wang, Chaoping, Zhou, Jie. "Strong-weak convergence of two algorithms for total asymptotically nonexpansive mappings." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2700--2709
Keywords
- Hilbert space
- convergence analysis
- iterative algorithm
- total asymptotically nonexpansive mappings
- projection.
MSC
References
-
[1]
R. P. Agarwal, X.-L. Qin, S. M. Kang, An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2011 (2011), 17 pages.
-
[2]
Y. I. Alber, C. E. Chidume, H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2006 (2006), 20 pages.
-
[3]
I. K. Argyros, S. George, S. M. Erappa, Expanding the applicability of the generalized Newton method for generalized equations, Commun. Optim. Theory, 2017 (2017), 12 pages.
-
[4]
B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X.-L. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 14 pages.
-
[5]
R. Bruck, T. Kuczumow, S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math., 65 (1993), 169–179.
-
[6]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2014), 103–120.
-
[7]
S. Y. Cho, B. A. Bin Dehaish, X.-L. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427–438.
-
[8]
S. Y. Cho, W.-L. Li, S. M. Kang, Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., 2013 (2013), 14 pages.
-
[9]
N.-N. Fang, Y.-P. Gong, Viscosity iterative methods for split variational inclusion problems and fixed point problems of a nonexpansive mapping , Commun. Optim. Theory, 2016 (2016), 15 pages.
-
[10]
A. Genel, J. Lindenstrauss, An example concerning fixed points, Israel J. Math., 22 (1975), 81–86.
-
[11]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174.
-
[12]
Z.-Y. Huang, Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 37 (1999), 1–7.
-
[13]
S. H. Khan, H. Fukhar-ud-din, Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal., 61 (2005), 1295–1301.
-
[14]
J. K. Kim, S. Y. Cho, X.-L. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Sci. Ser. B Engl. Ed., 31 (2011), 2041–2057.
-
[15]
M. Maiti, M. K. Ghosh, Approximating fixed points by Ishikawa iterates, Bull. Austral. Math. Soc., 40 (1989), 113–117.
-
[16]
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591–597.
-
[17]
H. Piri, R. Yavarimehr, Solving systems of monotone variational inequalities on fixed point sets of strictly pseudocontractive mappings, J. Nonlinear Funct. Anal., 2016 (2016), 18 pages.
-
[18]
X.-L. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive Banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488–502.
-
[19]
X.-L. Qin, S. Y. Cho, L. Wang, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 10 pages.
-
[20]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 9 pages.
-
[21]
S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67 (1979), 274–276.
-
[22]
J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407–413.
-
[23]
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43 (1991), 153–159.
-
[24]
K.-K. Tan, H.-K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301–308.
-
[25]
H. Zegeye, W. W. Kassu, M. G. Sangago, Common fixed points of a finite family of multi-valued rho-nonexpansive mappings in modular function spaces, Commun. Optim. Theory, 2016 (2016), 14 pages.