On enhanced k-fold averaged map of weak enriched F-contraction with application to boundary layer model

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.