SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 48, Issue 3, 2011, pp.575-584
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2011.48.3.575

Title & Authors

SOME NOTES ON ISHIKAWA ITERATION FOR MULTI-VALUED MAPPINGS

Song, Yisheng; Cho, Yeol-Je;

Song, Yisheng; Cho, Yeol-Je;

Abstract

In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838-844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.

Keywords

multi-valued mapping;strong convergence;Ishikawa iteration;

Language

English

Cited by

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

References

1.

B. Panyanak, Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. Math. Appl. 54 (2007), no. 6, 872-877.

2.

K. P. R. Sastry and G. V. R. Babu, Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point, Czechoslovak Math. J. 55(130) (2005), no. 4, 817-826.

3.

C. Shiau, K. K. Tan, and C. S. Wong, Quasi-nonexpansive multi-valued maps and selections, Fund. Math. 87 (1975), 109-119.

4.

N. Shahzad and H. Zegeye, On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71 (2009), no. 3-4, 838-844.