Iterated function systems in partial metric spaces with applications

Abstract

The mathematical study of fractals is deeply embedded in iterated function systems (IFS) formulated by Hutchinson in 1981. Since then, the development of iterated function systems in metric space setup, has caught the attention of many researchers. In the current work, the scope of iterated function systems is extended to more generalized settings such as partial metric spaces, Hausdor semi-metric spaces, and G-metric spaces. The existence and uniqueness of new attractors and common attractors of generalized iterated function systems in various spaces is proved with the assistance of generalized and generalized cyclic contractive mappings. Well-posedness of attractor based problems of the Hutchinson operators is established. Applications to dynamic programming and nonlinear integral equations are presented.