Viscosity iterative method for split common null point problems and fixed point problems
-
2032
Downloads
-
4222
Views
Authors
Yanlai Song
- College of Science, Zhongyuan University of Technology, 450007 Zhengzhou, China.
Xinhong Chen
- College of Science, Zhongyuan University of Technology, 450007 Zhengzhou, China.
Abstract
In this paper, we introduce and study
an Ishikawa-like iterative algorithm to approximate a common solution of a split common null point problem and a fixed point problem of asymptotically
pseudo-contractive mappings in the intermediate sense on unbounded domains.
We prove that the sequence generated by the iterative scheme strongly converges to
a common solution of the above-said problems. The method in this paper is novel and different from those given
in many other papers. The results are the extension and improvement
of the recent results in the literature.
Share and Cite
ISRP Style
Yanlai Song, Xinhong Chen, Viscosity iterative method for split common null point problems and fixed point problems, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 2, 86--101
AMA Style
Song Yanlai, Chen Xinhong, Viscosity iterative method for split common null point problems and fixed point problems. J. Nonlinear Sci. Appl. (2019); 12(2):86--101
Chicago/Turabian Style
Song, Yanlai, Chen, Xinhong. "Viscosity iterative method for split common null point problems and fixed point problems." Journal of Nonlinear Sciences and Applications, 12, no. 2 (2019): 86--101
Keywords
- Banach space
- split common null point problem
- fixed point
- metric resolvent
- asymptotically pseudocontractive mapping in the intermediate sense
MSC
References
-
[1]
Y. I. Alber, Metric and generalized projections operators in Banach spaces: properties and applications, Dekker, New York (1996)
-
[2]
K. Aoyama, F. Kohsaka, W. Takahashi, Three generalizations of firmly nonexpansive mappings: their relations and continuous properties , J. Nonlinear Convex Anal., 10 (2009), 131–147.
-
[3]
V. Barbu , Nonlinear Semigroups and Differential Equations in Banach spaces, Noordhoff International Publishing, Leiden (1976)
-
[4]
F. E. Browder , Nonlinear maximal monotone operators in Banach spaces, Math. Ann., 175 (1968), 89–113.
-
[5]
S. Y. Cho, Strong convergence analysis of a hybrid algorithm for nonlinear operators in a Banach space, J. Appl. Anal. Comput., 8 (2018), 19–31.
-
[6]
J. Deepho, P. Thounthong, P. Kumam, S. Phiangsungnoen, A new general iterative scheme for split variational inclusion and fixed point problems of k-strict pseudo-contraction mappings with convergence analysis, J. Comput. Appl. Math., 318 (2017), 293–306.
-
[7]
C.-S. Ge, A hybrid algorithm with variable coefficients for asymptotically pseudocontractive mappings in the intermediate sense on unbounded domains, Nonlinear Anal., 75 (2012), 2859–2866.
-
[8]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings , Proc. Amer. Math. Soc., 35 (1972), 171–174.
-
[9]
T.-H. Kim, H.-K. Xu , Convergence of the modified Mann’s iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal., 68 (2008), 2828–2836.
-
[10]
Q. H. Liu, Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Anal., 26 (1996), 1835–1842.
-
[11]
L. S. Liu , Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194 (1995), 114-125.
-
[12]
P.-E. Mainge , Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325 (2007), 469–479.
-
[13]
A. Moudafi , Krasnoselski-Mann iteration for hierarchical fixed-point problems, Inverse Problems, 23 (2007), 1635–1640.
-
[14]
J. O. Olaleru, G. A. Okeke, Strong convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense, British J. Math. Computer Sci., 2 (2012), 151–162.
-
[15]
X. 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.
-
[16]
X. Qin, S. Y. Cho, J. K. Kim , Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory Appl., 2010 (2010), 14 pages.
-
[17]
X. Qin, J.-C. Yao, Projection splitting algorithms for nonself operators, J. Nonlinear Convex Anal., 18 (2017), 925–935.
-
[18]
D. R. Sahu, H.-K. Xu, J.-C. Yao, Asymptotically strict pseudocontractive mappings in the intermediate sense, Nonlinear Anal., 70 (2009), 3502–3511.
-
[19]
J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mapping , J. Math. Anal. Appl., 158 (1991), 407–413.
-
[20]
W. Takahashi , Convex Analysis and Approximation of Fixed Points, Yokohama Publ., Yokohama (2000)
-
[21]
W. Takahashi, Nonlinear Functional Analysis, Yokohama Publ., Yokohama (2000)
-
[22]
W. Takahashi, J.-C. Yao, Strong convergence theorems by hybrid methods for the split common null point problem in Banach spaces , Fixed Point Theory Appl., 2015 (2015), 13 pages.
-
[23]
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.
-
[24]
P. Tianchai, An approximate solution to the fixed point problems for an infinite family of asymptotically strictly pseudocontractive mappings in the intermediate sense, cocoercive quasivariational inclusions problems and mixed equilibrium problems in Hilbert spaces, Fixed Point Theory Appl., 2012 (2012), 26 pages.
-
[25]
I. Yamada, N. Ogura , Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings , Numer. Funct. Anal. Optim., 25 (2004), 619–655.
-
[26]
H. Zegeye, M. Robdera, B. Choudhary, Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense, Comput. Math. Appl., 62 (2011), 326–332.
-
[27]
H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contraction in Hilbert spaces, Nonlinear Anal., 70 (2009), 3140–3145.