Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces
-
1940
Downloads
-
3833
Views
Authors
Issara Inchan
- Department of Mathematics, Uttaradit Rajabhat University, Uttaradit, Thailand.
Abstract
The main objective of this work is to modify two hybrid projection algorithm. First, we prove the strongly convergence to common fixed points of a sequence \(\{x_{n}\}\) generated by the hybrid projection algorithm of two asymptotically nonexpansive mappings, second, we prove the strongly convergence of a sequence \(\{x_{n}\}\) generated by the hybrid projection algorithm of two asymptotically nonexpansive semigroups. Our main results extend and improve the results of Dong et al. [Q.-L. Dong, S. N. He, Y. J. Cho, Fixed Point Theory Appl., \(\textbf{2015}\) (2015), 12 pages].
Share and Cite
ISRP Style
Issara Inchan, Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 10, 621--633
AMA Style
Inchan Issara, Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces. J. Nonlinear Sci. Appl. (2019); 12(10):621--633
Chicago/Turabian Style
Inchan, Issara. "Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces." Journal of Nonlinear Sciences and Applications, 12, no. 10 (2019): 621--633
Keywords
- Asymptotically nonexpansive mappings
- asymptotically nonexpansive semigroup
- fixed point
MSC
- 46C05
- 47D03
- 47H09
- 47H10
- 47H20
References
-
[1]
Q.-L. Dong, S. N. He, Y. J. Cho, A new hybrid algorithm and numerical realization for two nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 12 pages
-
[2]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171--174
-
[3]
I. Inchan, S. Plubtieng, Strong convergence theorems of hybrid methods for two asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. Hybrid Syst., 2 (2008), 1125--1135
-
[4]
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147--150
-
[5]
T.-H. Kim, H.-K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear. Anal., 64 (2006), 1140--1152
-
[6]
P.-K. Lin, K.-K. Tan, H. K. Xu, Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings, Nonlinear. Anal., 24 (1995), 929--946
-
[7]
W. A. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506--510
-
[8]
C. Martinez-Yanes, H.-K. Xu, Strong convergence of the CQ method for fixed point processes, Nonlinear Anal., 64 (2006), 2400--2411
-
[9]
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591--597
-
[10]
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Amer. Math. Soc., 43 (1991), 153--159
-
[11]
W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 341 (2008), 276--286
-
[12]
H.-K. Xu, Strong asymptotic behavior of almost-orbits of nonlinear semigroups, Nonlinear. Anal., 46 (2001), 135--151