Browse > Article
http://dx.doi.org/10.7468/jksmeb.2020.27.1.61

SOME STABILITY RESULTS FOR COINCIDENCE POINT ITERATIVE ALGORITHMS WITH THREE MAPPINGS  

Kim, Seung-Hyun (Department of Mathematics, Kyungsung University)
Kang, Mee-Kwang (Department of Mathematics, Dongeui University)
Publication Information
The Pure and Applied Mathematics / v.27, no.1, 2020 , pp. 61-70 More about this Journal
Abstract
In this paper, we introduce a new concept of stability of coincidence iterative algorithm for three mappings and derive a new three-step Jungck-type iterative algorithm. And, we prove a stability result and a strong convergence result for the Jungck-type algorithm using the MJ-contractive condition. Our results extend and unify the corresponding ones in [3, 6, 7, 13].
Keywords
stability; coincidence point; iterative algorithm;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A.M. Harder & T.L. Hicks: Stability results for fixed point iteration procedures. Math. Japonica 33 (1988), no. 5, 693-706.
2 S. Ishikawa: Fixed point by a new iteration method. Proc. Amer. Math. Soc. 44 (1974), no. 1, 147-150.   DOI
3 G. Jungck: Commuting mapping and fixed points. Amer. Math. Monthly 83 (1976), no. 4, 261-263.   DOI
4 W.R. Mann: Mean value methods in itewration. Proc. Amer. Math. Soc. 4 (1953), 506-510.   DOI
5 M.A. Noor, T.M. Rassias & Z. Huang: Three-stpe iterations for nonlinear accretive operator equations. J. Math. Anal. Appl. 274 (2002), 59-68.   DOI
6 M.O. Olatinwo: Some stability and convergence results for Picard, Mann, Ishikawa and Jungck type iterative algorithms for Akram-Zafar-Siddiqui type contraction mappings. Nonlinear Anal. Forum 21 (2016), no. 1, 65-75.
7 M.O. Olatinwo: Some stability and strong convergence results for the Jungck-Ishikawa iteration process. Creat. Math. Inform. 17 (2008), 33-42.
8 M.O. Osilike: Some stability results for fixed point iteration procedures. J. Nigerian Math. Soc. 14/15 (1995), 17-29.
9 M.O. Osilike & A. Udomene: Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings. Indian J. Pure Appl. Math. 30 (1999), no. 12, 1229-1234.
10 L. Qihou: A convergence theorem of the sequence of Ishikawa iterates for quasi- contractive mappings. J. Math. Anal. Appl. 146 (1990), 301-305.   DOI
11 B.E. Rhoades: Fixed point theorems and stability results for fixed point iteration procedures. Indian J. Pure Appl. Math. 21 (1990), no. 1, 1-9.
12 B.E. Rhoades: Fixed point theorems and stability results for fixed point iteration procedures II. Indian J. Pure Appl. Math. 24 (1993), no. 11, 691-703.
13 S.L. Singh, C. Bhatnagar & S.N. Mishra: Stability of Jungck-type iterative procedures. Int. J. Math. Math. Sci. 2005:19 (2005), 3035-3043.
14 V. Verinde: On the stability of some fixed point procedures. Bul. Stiint. Univ. Baia Mare, Ser. B, Mathematica-Informatica 18 (2002), no. 1, 7-14.