Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3303
Abstract
In a recent paper, Yu et al. obtained convergence and stability results of the $K^{\ast }$ iterative method for quasi-strictly contractive mappings [An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography. AIMS Mathematics 2021; 6 (7): 6699-6714.]. To guarantee these convergence and stability results, the authors imposed some strong conditions on parametric control sequences which are used in the $K^{\ast }$ iterative method. The aim of the presented work is twofold: (a) to recapture the aforementioned results without any restrictions imposed on the mentioned parametric control sequences (b) to complete the work of Yu et al. by adding a result regarding the data dependency of the fixed points of quasi-strictly contractive mappings. We also furnish some illustrative examples to support our results. Our work can be considered an important refinement and complement of the work of Yu et al.
Keywords
Iterative methods, fixed points, convergence, stability, data dependency, quasi-strictly contractive mappings
First Page
2819
Last Page
2833
Recommended Citation
ÇELİK, RUKEN and ŞİMŞEK, NECİP
(2022)
"Some convergence, stability, and data dependence results for $K^{\ast }$ iterative method of quasi-strictly contractive mappings,"
Turkish Journal of Mathematics: Vol. 46:
No.
7, Article 17.
https://doi.org/10.55730/1300-0098.3303
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss7/17
