scholarly journals Applications of Multivalued Contractions on Graphs to Graph-Directed Iterated Function Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
T. Dinevari ◽  
M. Frigon
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Iterated Function System ◽  
Iterated Function Systems ◽  
Complete Metric Spaces ◽  
Fixed Point Result ◽  
Iterated Function ◽  
Multivalued Contractions

We apply a fixed point result for multivalued contractions on complete metric spaces endowed with a graph to graph-directed iterated function systems. More precisely, we construct a suitable metric space endowed with a graphGand a suitableG-contraction such that its fixed points permit us to obtain more information on the attractor of a graph-directed iterated function system.

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

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 967 ◽  
Author(s):  
Sudesh Kumari ◽  
Renu Chugh ◽  
Jinde Cao ◽  
Chuangxia Huang
Keyword(s):  
Inverse Problem ◽  
Fixed Points ◽  
Natural Number ◽  
Metric Space ◽  
Metric Spaces ◽  
Iterated Function System ◽  
Hausdorff Metric ◽  
Iterated Function Systems ◽  
Iterated Function ◽  
Collage Theorem

In this paper, we obtain multifractals (attractors) in the framework of Hausdorff b-metric spaces. Fractals and multifractals are defined to be the fixed points of associated fractal operators, which are known as attractors in the literature of fractals. We extend the results obtained by Chifu et al. (2014) and N.A. Secelean (2015) and generalize the results of Nazir et al. (2016) by using the assumptions imposed by Dung et al. (2017) to the case of ciric type generalized multi-iterated function system (CGMIFS) composed of ciric type generalized multivalued G-contractions defined on multifractal space C ( U ) in the framework of a Hausdorff b-metric space, where U = U 1 × U 2 × ⋯ × U N , N being a finite natural number. As an application of our study, we derive collage theorem which can be used to construct general fractals and to solve inverse problem in Hausdorff b-metric spaces which are more general spaces than Hausdorff metric spaces.

scholarly journals Some new types multivalued F-contractions on quasi metric spaces and their fixed points

2019 ◽  
Vol 35 (1) ◽  
pp. 41-50
Author(s):  
HATICE ASLAN HANCER ◽  
◽  
MURAT OLGUN ◽  
ISHAK ALTUN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Fixed Point Result ◽  
Q Function

In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued Fd-contraction on quasi metric space (X, d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space.

scholarly journals Unique Fixed Point Theorem for Weakly C-Contractive Mappings

1970 ◽  
Vol 5 (1) ◽  
pp. 6-13 ◽  
Author(s):  
Binayak S Choudhury
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Engineering And Technology ◽  
Existing Result

In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces. Key words: Metric space; Fixed point; Weak C-contraction. M S C (2000): 54H25   DOI: 10.3126/kuset.v5i1.2842 Kathmandu University Journal of Science, Engineering and Technology Vol.5, No.1, January 2009, pp 6-13

scholarly journals Fixed points of multivalued nonlinear F-contractions on complete metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Ishak Altun ◽  
Gülhan Mınak ◽  
Murat Olgun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Maps ◽  
Famous Theorem ◽  
Complete Metric Spaces ◽  
Fixed Point Result ◽  
Proper Generalization

We introduce a new concept for multivalued maps, also called multivalued nonlinear F-contraction, and give a fixed point result. Our result is a proper generalization of some recent fixed point theorems including the famous theorem of Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334(1):132–139, 2007].

scholarly journals Fixed points in k complete metric spaces

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Luljeta Kikina ◽  
Kristaq Kikina
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Spaces

AbstractA fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [

scholarly journals Fixed points of multivalued contractions via generalized class of simulation functions

2019 ◽  
Vol 38 (3) ◽  
pp. 161-176
Author(s):  
Deepesh Kumar Patel
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Simulation Functions ◽  
Multivalued Contractions

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in α-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well known fixed point results of the literature. Some examples and consequence are given to  illustrate the usability of the theory.

The Hutchinson-Barnsley theory for infinite iterated function systems

2005 ◽  
Vol 72 (3) ◽  
pp. 441-454 ◽  
Author(s):  
Gertruda Gwóźdź-Lukawska ◽  
Jacek Jachymski
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Iterated Function System ◽  
Complete Metric Space ◽  
Iterated Function Systems ◽  
Function System ◽  
Iterated Function ◽  
Infinite Case

We show that some results of the Hutchinson-Barnsley theory for finite iterated function systems can be carried over to the infinite case. Namely, if {Fi:i∈ ℕ} is a family of Matkowski's contractions on a complete metric space (X, d) such that (Fix0)i∈Nis bounded for somex0∈X, then there exists a non-empty bounded and separable setKwhich is invariant with respect to this family, that is,. Moreover, given σ ∈ ℕℕandx∈X, the limit exists and does not depend onx. We also study separately the case in which (X, d) is Menger convex or compact. Finally, we answer a question posed by Máté concerning a finite iterated function system {F1,…,FN} with the property that each ofFihas a contractive fixed point.

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

2017 ◽  
Vol 55 (2) ◽  
pp. 119-142
Author(s):  
Flavian Georgescu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Iterated Function Systems ◽  
Iterated Function ◽  
Convex Contractions

AbstractThe concept of generalized convex contraction was introduced and studied by V. Istrăţescu and the notion ofb-metric space was introduced by I. A. Bakhtin and S. Czerwik. In this paper we combine these two elements by studying iterated function systems consisting of generalized convex contractions on the framework ofb-metric spaces. More precisely we prove the existence and uniqueness of the attractor of such a system providing in this way a generalization of Istrăţescu’s convex contractions fixed point theorem in the setting of complete strongb-metric spaces.

scholarly journals Fixed points and sets of multivalued contractions: an advanced survey with some new results

2021 ◽  
Vol 22 (1) ◽  
pp. 15-30
Author(s):  
Jan Andres ◽  
Jiřı́ Fišer ◽  
Lech Górniewicz
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Absolute Retracts ◽  
Continuation Principle ◽  
Nonlinear Alternative ◽  
Multivalued Contractions ◽  
Fixed Point Sets ◽  
Coupled Fixed Points

The existence of fixed points and, in particular, coupled fixed points is investigated for multivalued contractions in complete metric spaces. Multivalued coupled fractals are furthermore explored as coupled fixed points of certain induced operators in hyperspaces, i.e. as coupled compact subsets of the original spaces. The structure of fixed point sets is considered in terms of absolute retracts. We also formulate a continuation principle for multivalued contractions as a nonlinear alternative based on the topological essentiality. Two illustrative examples about coupled multivalued fractals are supplied.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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