Some convergence, stability, and data dependence results for $K^{\ast }$ iterative method of quasi-strictly contractive mappings

Authors: RUKEN ÇELİK, NECİP ŞİMŞEK

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

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