RETRACTED: On multistep iterative scheme for approximating the common fixed points of contractive-like operators
type: Item
instance of: scholarly article
title: RETRACTED: On multistep iterative scheme for approximating the common fixed points of contractive-like operators
zbMATH Open document ID: 1478.47100
DOI: 10.1155/2010/530964
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2010-04-20T00:00:00Z
review text: Summary: We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of \textit{M. O. Olatinwo} [Creat. Math. Inform. 17, No. 1, 33--42 (2008; Zbl 1199.47282); with \textit{C. O. Imoru}, Acta Math. Univ. Comen., New Ser. 77, No. 2, 299--304 (2008; Zbl 1174.47056)]. Consequently, several results in the literature are generalized. Retraction notice: This article has been retracted as it is essentially identical in technical content with a previously published paper in [the authors, Fasc. Math. 45, 87--98 (2010; Zbl 1272.47084)].
Mathematics Subject Classification ID: 47J26
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5695253
zbMATH Keywords: Jungck-multistep iteration
zbMATH Keywords: strong convergence
zbMATH Keywords: generalized contractive-like operators
Wikidata QID: Q58651788
author: J. O. Olaleru
author: H. Akewe
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/530964
OpenAlex ID: W2027890526
cites work: Common fixed point results for noncommuting mappings without continuity in cone metric spaces
cites work: Q4680155
cites work: Q5182846
cites work: Some Results on Fixed Points--II
cites work: Some developments in general variational inequalities
cites work: Fixed point theorems in metric spaces
cites work: Mean Value Methods in Iteration
cites work: Fixed Points by a New Iteration Method
cites work: New approximation schemes for general variational inequalities
cites work: The equivalence between Mann-Ishikawa iterations and multistep iteration
cites work: Common Fixed Point Theorems for Commuting Maps on a Metric Space
cites work: Commuting Mappings and Fixed Points
cites work: Q4136193
cites work: Stability of Jungck-type iterative procedures
cites work: Q3520084
cites work: Q3639586
cites work: Q3620604
cites work: Approximation of common fixed points of weakly compatible pairs using the Jungck iteration
cites work: Q5427589
cites work: Q5446352
cites work: Comments on two fixed point iteration methods
cites work: Stability results for the Ishikawa fixed point iteration procedure
DBLP publication ID: journals/ijmmsc/OlaleruA10
description: scientific article; zbMATH DE number 5695253