Abstract and Applied Analysis

On the Convergence of Multistep Iteration for Uniformly Continuous Φ -Hemicontractive Mappings

Zhiqun Xue, Arif Rafiq, and Haiyun Zhou

Full-text: Open access

Abstract

It is shown that the convergence of the multistep iterative process with errors is obtained for uniformly continuous Φ -hemicontractive mappings in real Banach spaces. We also revise the problems of C. E. Chidume and C. O. Chidume (2005).

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 386983, 9 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475852

Digital Object Identifier
doi:10.1155/2012/386983

Mathematical Reviews number (MathSciNet)
MR2975356

Zentralblatt MATH identifier
06116384

Citation

Xue, Zhiqun; Rafiq, Arif; Zhou, Haiyun. On the Convergence of Multistep Iteration for Uniformly Continuous $\mathrm{\Phi }$ -Hemicontractive Mappings. Abstr. Appl. Anal. 2012 (2012), Article ID 386983, 9 pages. doi:10.1155/2012/386983. https://projecteuclid.org/euclid.aaa/1364475852


Export citation

References

  • B. E. Rhoades and S. M. Soltuz, “The equivalence between Mann-Ishikawa iterations and multistep iteration,” Nonlinear Analysis: Theory, Methods & Applications, vol. 58, no. 1-2, pp. 219–228, 2004.
  • Y. Xu, “Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations,” Journal of Mathematical Analysis and Applications, vol. 224, no. 1, pp. 91–101, 1998.
  • C. E. Chidume and C. O. Chidume, “Convergence theorems for fixed points of uniformly continuous generalized $\Phi $-hemi-contractive mappings,” Journal of Mathematical Analysis and Applications, vol. 303, no. 2, pp. 545–554, 2005.
  • K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
  • C. Moore and B. V. C. Nnoli, “Iterative solution of nonlinear equations involving set-valued uniformly accretive operators,” Computers & Mathematics with Applications, vol. 42, no. 1-2, pp. 131–140, 2001.