Abstract
This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α -Krasnosel’skiĭ mapping associated with b -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b -enriched quasinonexpansive mappings have been proved.
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