Some Results on an Iterative Algorithm Associated with Enriched Contractions in Banach Spaces
Abstract
In this study, the Picard-S algorithm, which is generated by the average mapping classes defined by the enriched contractions in Banach spaces, is considered. Using these mapping classes, the convergence of the iterative sequence obtained from the Picard-S algorithm to the fixed point of the enriched contraction has been obtained without any additional conditions on the control sequences. It has been shown that the convergence of the iterative sequences generated by Picard-S and the CR algorithms with these mapping classes to the fixed point is equivalent, and a result regarding the data dependency of the Picard-S algorithm for the same mapping classes has been obtained. All results obtained are supported by numerical examples in infinite-dimensional Banach spaces.
Keywords
Banach Space, Average Mapping, Fixed Point, Enriched Mapping
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