On Contraction Principles in Product Spaces and Applications in Iterated Function Systems

This paper develops an extension of the research work by Proinov to the product spaces X|I| (I is representing an indexing set). This paper also introduces a novel class of (L;Y)-contractions defined on a supremum metric (X|I|,d′). In supremum metric (X|I|,d′), several new fixed point theorems for (L;Y)-contractions have been established that generalize well-known ideas like the Banach, Geraghty, Boyd–Wong, and Wardowski principles. This paper also contributes a new iterated function system (IFS) built on the family of (L;Y)-contractions and demonstrates the existence and uniqueness of fractals (in other words, compact attractors) in a complete supremum metric (X|I|,d′). Theoretical work is illustrated with examples and graphs.