Abstract

In this short note we prove the existence of local fractal functions of the Orlicz-Sobolev class of order $m\geq 0.$ The graph of a local fractal function coincides with the attractor of an appropriate iterated function system, whose construction is fairly standard. Local fractal functions appear naturally as the fixed points of the Read-Bajraktarević operator when restricted to a suitable Orlicz-Sobolev space. Our results extend some of the outcomes obtained by Massopust on Lebesgue and Sobolev spaces to higher order, dimension and function spaces (where the role of the norm is now played by a Young function).

Keywords: Fractal; attractor; iterated function system (IFS); Orlicz-Sobolev space; Read-Bajraktarević operator; contractive map.

MSC: 28A80, 35J60, 37C70, 37G35, 46E30

DOI: 10.57016/MV-v49CIA71

Pages:  210--220     

Volume  77 ,  Issue  3 ,  2025