Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Abstract

The aim of this paper is to construct a fractal with the help of a finite family of generalized F -contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize and extend various results in the existing literature.---------------

Multi Fractals of Generalized Multivalued Iterated Function Systems in b-Metric Spaces with Applications

“…The idea of a b-metric space was given by Czerwik [35]. This opened a new door for researchers and they published several research papers of fixed point theory (see, e.g., [35][36][37][38]). Kamran et al [39] and Ali et al [40] introduced F-contraction mappings in the framework of b metric spaces.…”

“…Secelean [42] considered the generalized iterated function systems, defined on product of metric spaces to improve some fixed point results. Dung et al [43] revised the results of Nazir et al [37,44] by adding a commutativity assumption on the maps. Inspired by their work, we attempt to extend their results to find the multifractals using ciric type generalized multivalued G-contraction mappings in the framework of Hausdorff b-metric spaces.…”

Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

“…-to consider more general domains or ranges of the iterated function systems (see, for example, [6], [10], [13], [14], [24], [30], [33] and [45]). …”

“…-to work with more general contractive conditions on the constitutive functions of the iterated function systems (see, for example, [18], [34], [36], [37], [38], [39], [45], [48], [52], [53], [57] and [58]). …”

“…Concerning the first line of generalization, we emphasize the papers [10], [14] and [45], were iterated function systems in the setting of b-metric spaces are studied. The notion of b-metric space was introduced by I.…”