Iterative computation of fixed points of quasi-asymptotic pseudo-contractions
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Authors
Yonghong Yao
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, P. R. China.
Xiaoxue Zheng
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, P. R. China.
Limin Leng
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, P. R. China.
Yeong-Cheng Liou
- Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Kaohsiung 80708, Kaohsiung 80708, Taiwan.
Abstract
An iterative algorithm is presented to find the fixed points of a quasi-asymptotic pseudo-contraction in
Hilbert spaces. It is shown that the proposed algorithm converges strongly to the fixed point of a quasiasymptotic
pseudo-contraction.
Share and Cite
ISRP Style
Yonghong Yao, Xiaoxue Zheng, Limin Leng, Yeong-Cheng Liou, Iterative computation of fixed points of quasi-asymptotic pseudo-contractions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4580--4588
AMA Style
Yao Yonghong, Zheng Xiaoxue, Leng Limin, Liou Yeong-Cheng, Iterative computation of fixed points of quasi-asymptotic pseudo-contractions. J. Nonlinear Sci. Appl. (2016); 9(6):4580--4588
Chicago/Turabian Style
Yao, Yonghong, Zheng, Xiaoxue, Leng, Limin, Liou, Yeong-Cheng. "Iterative computation of fixed points of quasi-asymptotic pseudo-contractions." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4580--4588
Keywords
- Quasi-asymptotic pseudo-contraction
- fixed point
- iterative algorithm
- Hilbert spaces.
MSC
References
-
[1]
L. C. Ceng, H. K. Xu, J. C. Yao, The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal., 69 (2008), 1402-1412.
-
[2]
C. E. Chidume, H. Zegeye, Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings, J. Math. Anal. Appl., 278 (2003), 354-366.
-
[3]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174.
-
[4]
P. E. Mainge , Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325 (2007), 469-479.
-
[5]
M. O. Osilike, S. C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling, 32 (2000), 1181-1191.
-
[6]
J. Schu , Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407-413.
-
[7]
N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal., 64 (2006), 558-567.
-
[8]
T. Shimizu, W. Takahashi , Strong convergence theorem for asymptotically nonexpansive mappings, Nonlinear Anal., 26 (1996), 265-272.
-
[9]
H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256.
-
[10]
Y. Yao, R. P. Agarwal, M. Postolache, Y. C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory Appl., 2014 (2014), 14 pages.
-
[11]
Y. Yao, Y. C. Liou, J. C. Yao , Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction, Fixed Point Theory Appl., 2015 (2015), 19 pages.
-
[12]
Y. Yao, G. Marino, H. K. Xu, Y. C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 14 pages.
-
[13]
Y. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory Appl., 2014 (2014), 13 pages.
-
[14]
Y. Yao, M. Postolache, Y. C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., 2013 (2013), 12 pages.
-
[15]
Y. Yao, N. Shahzad , New methods with perturbations for non-expansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2011 (2011), 9 pages.
-
[16]
H. Zegeye, N. Shahzad, Strong convergence theorems for continuous semigroups of asymptotically nonexpansive mappings, Numer. Funct. Anal. Optim., 30 (2009), 833-848.
-
[17]
H. Zegeye, N. Shahzad, Y. Yao, Minimum-norm solution of variational inequality and fixed point problem in Banach spaces, Optimization, 64 (2015), 453-471.
-
[18]
H. Zhou , Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 3140-3145.
-
[19]
H. Zhou, Y. Su , Strong convergence theorems for a family of quasi-asymptotic pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 4047-4052.