A NOVEL CLASSIFICATION of FRACTALS VIA GENERALIZED (w, ℱ) -HUTCHINSON OPERATORS and THEIR APPLICATIONS

This paper explores a novel framework for generating fractals using generalized (w,ℱ)-Hutchinson operators, an extension of the classical (w,ℱ)-contraction mappings. By employing a finite group of these generalized operators, we are able to produce fractals with complex and nuanced properties that surpass those generated by standard contraction mappings in Banach spaces. We investigate the influence of varying contractive conditions on the resulting fractal structures and apply these concepts within iterated function systems. Through various illustrative examples, we demonstrate the effectiveness of our approach and highlight how it enhances and builds upon existing research in fractal theory and iterated function systems.