Journal ArticleDOI
Multivalued fractals in b-metric spaces
TLDR
In this article, the authors extend the study of fractal operator theory for multivalued operators on complete b-metric spaces to the case of complete or compact metric spaces.Abstract:
Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.read more
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Journal ArticleDOI
Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces
TL;DR: In this article, the generalized weak contractive condition in partially ordered complete b-metric spaces was shown to hold for four mappings satisfying generalized weak contractsive condition, and the results extended and improved several comparable results in existing literature.
Journal ArticleDOI
A Generalization of b-Metric Space and Some Fixed Point Theorems
TL;DR: In this article, the concept of extended b-metric space is introduced, inspired by the concepts of b-means and b-space, and some fixed point theorems for self-mappings defined on such spaces are established.
Journal ArticleDOI
Partial b-Metric Spaces and Fixed Point Theorems
TL;DR: In this paper, the concept of partial b-metric spaces is introduced as a generalization of partial metric and b-measure spaces, and an analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces.
Journal ArticleDOI
A generalized metric space and related fixed point theorems
Mohamed Jleli,Bessem Samet +1 more
TL;DR: In this article, the authors introduce a new concept of generalized metric spaces for which they extend some well-known fixed point results including Banach contraction principle, Ciric fixed point theorem, Ran and Reurings, and a fixed point result due to Nieto and Rodriguez-Lopez.
Journal ArticleDOI
New fixed point theorems for set-valued contractions in b-metric spaces
Radu Miculescu,Alexandru Mihail +1 more
TL;DR: In this article, the authors generalize a series of fixed point results in the framework of b-metric spaces and exemplify it by extending Nadler's contraction principle for set-valued functions.
References
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Book
Fractals Everywhere
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
Book
Lectures on Analysis on Metric Spaces
TL;DR: Theoretically, doubling measures and quasisymmetric maps have been studied in the context of Euclidean spaces in this article, where doubling measures have been shown to be equivalent to Poincare inequalities.