Some Fixed Point Results for Fractals of Interpolative Ćirić–Reich–Rus Mappings in b-Metric Spaces

In this paper, we introduce the concept of a (λσ,ϖ1σ,ϖ2σ)-interpolative Ćirić–Reich–Rus contraction iterated function system and an iterated multivalued system using interpolative Ćirić–Reich–Rus operators. The objective of this paper is to construct fractals using the Hutchinson operator and Hutchinson-like operator involving interpolative Ćirić–Reich–Rus contraction mappings, which extend the class of classical contractions, in b-metric space. The use of interpolative Ćirić–Reich–Rus contraction guarantees unique fractal attractors, thereby playing a vital role in the analysis of geometric structures and their wide-range applications in scientific and engineering fields. Using the above new definitions, we present a version of the Collage theorem adapted to iterated function systems satisfying interpolative Ćirić–Reich–Rus contractions. Further, we study the well-posedness of the new interpolative Ćirić–Reich–Rus contraction-iterated function system-Hutchinson problem. Our findings unify, generalize, and extend various earlier results reported in the literature.