Fixed points and attractors of iterated function systems via generalized enriched Kannan-type cyclic contractions

In the context of Banach spaces, we present a new and more general class of generalized enriched Kannan-type cyclic contraction mapping and prove relevant fixed point theorems. Our approach is distinct in that we use the Krasnoselskij iteration to approximate the fixed point, which allows us to generate explicit error estimates and convergence behaviours. We build generalized iterated function systems (IFS) produced by these enriched contractions and demonstrate the existence and uniqueness of their attractors as a novel application. The present study is unique in that it links classical contraction concepts to the theory of IFS and extends them to a more complex cyclic system. In addition to a numerical illustration, examples are provided to demonstrate the efficacy of our findings.