Generalized Multiparameter Enriched Cyclic Contractions With Maia and Randomized Versions: Theoretical Foundations and Application to Fractals

In this manuscript, we present the concept of a generalized multiparameter enriched cyclic contraction mapping and its randomized version in the framework of Banach spaces. A key aspect of our methodology involves the development of a multi‐averaged mapping. By employing this, we establish a fixed point theorem, where the mapping operates on the union of subsets of the original space. We further extend this concept to Maia‐type contractions. Additionally, we provide an application of our main result within the context of iterated function systems.