Abstract
The aim of this paper is to introduce a large class of mappings, called enriched Kannan mappings, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for the Krasnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces. We further extend these mappings to the class of enriched Bianchini mappings. Examples to illustrate the effectiveness of our results are given. As applications of our main fixed point theorems, we present two Krasnoselskij projection type algorithms for solving split feasibility problems and variational inequality problems in the class of enriched Kannan mappings and enriched Bianchini mappings, respectively.
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