On Enhanced k-Fold Averaged Map of Weak Enhanced f-Contraction with Application to Boundary Layer Model
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Date
2025
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Publisher
SCIK Publishing Cooperation.
Abstract
Recently, two separate generalizations of enriched contraction maps, namely, weak enriched contraction
and weak enriched F-contractions, were introduced to approximate fixed points using the higher order Kirk iteration.
In this article, we introduce an enhanced k-fold averaged iterative procedure that can approximate fixed points
of operators that may not meet the hypotheses of the previous k-fold averaged iterative scheme for each k. Our
first attempt is to prove the strong convergence and stability of the enhanced k-fold averaged iteration associated
with the weak enriched F-contraction in Banach spaces. Also, we justify the equivalence of the enhanced k-fold
Kirk iteration with other comparable iterative schemes using the weak enriched F-contractive map. Furthermore,
we show the validation and versatility of the enhanced map with some numerical examples. The results indicate
that the improved k-fold averaged iteration (a) has a better convergent rate than others and (b) exhibits contracting
behavior when others fail for some enriching constants. As an application, the enhanced k-fold map is employed
to solve a boundary layer model.
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Citation
https://doi.org/10.28919/afpt/9127