A transformation algorithm for nonexpansive mappings

Volume 10, Issue 5, pp 2449--2456 http://dx.doi.org/10.22436/jnsa.010.05.15

Publication Date: May 25, 2017 Submission Date: March 21, 2017

Download PDF

Download XML

2054 Downloads
3022 Views

Authors

Xinhe Zhu - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China. Shin Min Kang - Center for General Education, China Medical University, Taichung 40402, Taiwan. - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea.

Abstract

A transformation algorithm is constructed for finding the fixed points of nonexpansive mappings. We show that the suggested algorithm converges strongly to a fixed point of nonexpansive mappings under some different control conditions.

Share and Cite

ISRP Style

Xinhe Zhu, Shin Min Kang, A transformation algorithm for nonexpansive mappings, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2449--2456

AMA Style

Zhu Xinhe, Kang Shin Min, A transformation algorithm for nonexpansive mappings. J. Nonlinear Sci. Appl. (2017); 10(5):2449--2456

Chicago/Turabian Style

Zhu, Xinhe, Kang, Shin Min. "A transformation algorithm for nonexpansive mappings." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2449--2456

Keywords

Iterative method
nonexpansive mapping
fixed point.

MSC

47H10
47H09

References

[1] M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H.-K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014 ), 9 pages.
- View Article
- Google Scholar

[2] K. Goebel, W. A. Kirk, Topics in Metric Fixed Point Theory: Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
- Google Scholar

[3] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73 (1967), 957-961

[4] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147–150.

[5] P.-L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris Ser. A-B, 284 (1977), 1357–1359.

[6] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506–510.

[7] A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46–55.
- View Article
- Google Scholar

[8] T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl., 2005 (2005), 103–123.

[9] H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240–256.
- View Article
- Google Scholar

[10] H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279–291.
- View Article
- Google Scholar

[11] H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 12 pages.

[12] Y.-H. Yao, R.-D. Chen, J.-C. Yao, Strong convergence and certain control conditions for modified Mann iteration, Nonlinear Anal., 68 (2008), 1687–1693.

[13] Y.-H. Yao, Y.-C. Liou, T.-L. Lee, N.-C. Wong, An iterative algorithm based on the implicit midpoint rule for nonexpansive mappings, J. Nonlinear Convex Anal., 17 (2016), 655–668.

[14] Y.-H. Yao, N. Shahzad, New methods with perturbations for nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2011 (2011), 9 pages.

[15] Y.-H. Yao, N. Shahzad, Viscosity implicit midpoint methods for nonexpansive mappings, J. Nonlinear Sci. Appl., (In press),

[16] Y.-H. Yao, N. Shahzad, Y.-C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 15 pages.