Nonlinear Relation-Theoretic Suzuki-Generalized Ćirić-Type Contractions and Application to Fractal Spaces (original) (raw)

Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems

Symmetry

The purpose of this paper is to define the notion of extended convex ℱ contraction by imposing less conditions on the function ℱ satisfying certain contractive conditions. We prove the existence of fixed points for these types of mappings in the setting of b-metric spaces. In addition, some illustrative examples are provided to show the usability of the obtained results. Lastly, we use the obtained fixed-point results to find the fractals with respect to the iterated function systems in the framework of b-metric spaces. Furthermore, the variables involved in the b-metric space are symmetric, and symmetry plays an important role in solving the nonlinear problems defined in operator theory.

Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

Analele Universitatii "Ovidius" Constanta - Seria Matematica

The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved.

Fixed Point Theorems and Iterative Function System in G-Metric Spaces

JOURNAL OF UNIVERSITY OF BABYLON for pure and applied sciences, 2019

In this paper, we introduce the Hutchinson Barnsley operator (shortly, operator) on a metric space and employ its theory to construct a fractal set as its unique fixed point by using Ciric type generalized -contraction in complete metric space. Some concepts are illustrated by numerical examples.

A Suzuki-type fixed point theorem for nonlinear contractions

2012

We introduce the notion of admissible functions and show that the family of L-functions introduced by Lim in [Nonlinear Anal. 46(2001), 113--120] and the family of test functions introduced by Geraghty in [Proc. Amer. Math. Soc., 40(1973), 604--608] are admissible. Then we prove that if phi\phiphi is an admissible function, (X,d)(X,d)(X,d) is a complete metric space, and TTT is a mapping on XXX such that, for alpha(s)=phi(s)/s\alpha(s)=\phi(s)/salpha(s)=phi(s)/s, the condition 1/(1+alpha(d(x,Tx)))d(x,Tx)<d(x,y)1/(1+\alpha(d(x,Tx))) d(x,Tx) < d(x,y)1/(1+alpha(d(x,Tx)))d(x,Tx)<d(x,y) implies d(Tx,Ty)<phi(d(x,y))d(Tx,Ty) < \phi(d(x,y))d(Tx,Ty)<phi(d(x,y)), for all x,yinXx,y\in Xx,yinX, then TTT has a unique fixed point. We also show that our fixed point theorem characterizes the metric completeness of XXX.