Taiwanese Journal of Mathematics

ITERATION SCHEME FOR A PAIR OF SIMULTANEOUSLY ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

Jun Li, Jong Kyu Kim, and Nan Jing Huang

Full-text: Open access

Abstract

We introduce the notion of a pair of simultaneously asymptotically quasi-nonexpansive type mappings and prove a general strong convergence theorem of the iteration scheme with errors for a pair of simultaneously asymptotically quasi-nonexpansive type mappings in Banach spaces. The result of this paper is an extension and an improvement of the corresponding well known results.

Article information

Source
Taiwanese J. Math., Volume 10, Number 6 (2006), 1419-1429.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404565

Digital Object Identifier
doi:10.11650/twjm/1500404565

Mathematical Reviews number (MathSciNet)
MR2275136

Zentralblatt MATH identifier
1128.47057

Subjects
Primary: 47H05: Monotone operators and generalizations 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 49M05: Methods based on necessary conditions

Keywords
scheme with errors a pair of simultaneously asymptotically quasi-nonexpansive type mappings common fixed points stability

Citation

Li, Jun; Kim, Jong Kyu; Huang, Nan Jing. ITERATION SCHEME FOR A PAIR OF SIMULTANEOUSLY ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES. Taiwanese J. Math. 10 (2006), no. 6, 1419--1429. doi:10.11650/twjm/1500404565. https://projecteuclid.org/euclid.twjm/1500404565


Export citation

References

  • [1.] S. S. Chang, On the approximating problem of fixed points for asymptotically nonexpansive mappings, Indian J. Pure and Appl., 32(9) 2001, 1-11.
  • [2.] S. S. Chang, J. K. Kim and S. M. Kang, Approximating fixed points of asymptotically quasi-nonexpansive type mappings by the Ishikawa iterative sequences with mixed errors, Dynamic Systems and Appl., 13 (2004), 179-186.
  • [3.] M. K. Ghosh and L. Debnath, Convergence of Ishikawa iterative of quasi-nonexpansive mappings, J. Math. Anal. Appl., 207 (1997), 96-103.
  • [4.] K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1) (1972), 171-174.
  • [5.] Z. Y. Huang, Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 37 (1999), 1-7.
  • [6.] J. K. Kim, K. H. Kim and K. S. Kim, Three-step iterative sequences with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces Nonlinear Analysis and Convex Analysis, RIMS Kokyuraku, Kyoto University, 1365 (2004), 156-165.
  • [7.] J. K. Kim, K. H. Kim and K. S. Kim, Convergence theorems of modified three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces, PanAmerican Math. Jour., 14(1) (2004), 45-54.
  • [8.] W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., 17 1974, 339-346.
  • [9.] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl., 259 (2001), 1-7.
  • [10.] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl., 259 (2001), 18-24.
  • [11.] Q. H. Liu, Iteration sequences for asymptotically quasi-nonexpansive mappings with error member of uniformly convex Banach spaces, J. Math. Anal. Appl., 266 (2002), 468-471.
  • [12.] W. V. Petryshyn and T. E. Williamson, Strong and weak convergence of the sequence of successive approximations for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl., 43 (1973), 459-497.
  • [13.] J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407-413.
  • [14.] K. K. Tan and H. K. Xu, Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 122(3) (1994), 733-739.
  • [15.] K. K. Tan and H. K. Xu, Approximating fixed point of nonexpansive mappings by the Ishikawa iterative process, J. Math. Anal. Appl., 178 (1993), 301-308.
  • [16.] L. C. Zeng, A note on approximating fixed points of nonexpansive mapping by the Ishikawa iterative processes, J. Math. Anal. Appl., 226 (1998), 245-250.