Browse > Article
http://dx.doi.org/10.4134/CKMS.2011.26.2.229

CONVERGENCE OF ISHIKAWA ITERATION WITH ERROR TERMS ON AN ARBITRARY INTERVAL  

Yuan, Qing (College of Science Hangzhou Normal University)
Cho, Sun-Young (Department of Mathematics Gyeongsang National University)
Qin, Xiaolong (College of Science Hangzhou Normal University)
Publication Information
Communications of the Korean Mathematical Society / v.26, no.2, 2011 , pp. 229-235 More about this Journal
Abstract
In this paper, a continuous real function on the real line is considered. The necessary and sufficient conditions for the convergence of the Ishikawa iteration with error terms for the functional are obtained.
Keywords
fixed point; real function; Mann iteration; Ishikawa iteration;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 D. Borwein and J. Borwein, Fixed point iterations for real functions, J. Math. Anal. Appl. 157 (1991), no. 1, 112-126.   DOI
2 R. L. Franks and R. P. Marzec, A theorem on mean value iterations, Proc. Amer. Math. Soc. 30 (1971), 324-326.   DOI   ScienceOn
3 S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150.   DOI   ScienceOn
4 W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510.   DOI   ScienceOn
5 Y. Qing and L. Qihou, The necessary and sufficient condition for the convergence of Ishikawa iteration on an arbitrary interval, J. Math. Anal. Appl. 323 (2006), no. 2, 1383-1386.   DOI   ScienceOn
6 B. E. Rhoades, Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc. 196 (1974), 161-176.   DOI