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

2019 ◽  
Vol 27 (2) ◽  
pp. 329-340
Author(s):  
Salwa Salman Abed ◽  
Anaam Neamah Faraj
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Generalized Contraction ◽  
Numerical Examples ◽  
Iterated Function ◽  
Self Similar

Iterated function space is a method to construct fractals and the results are self-similar. 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. In addition, some concepts are illustrated by numerical examples.

SOME FIXED POINT THEOREMS

2011 ◽  
Vol 08 (01) ◽  
pp. 1-8 ◽  
Author(s):  
M. A. AHMED
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Generalized Contraction

This paper has three objectives. First, we establish a fixed point theorem for a generalized contraction in dislocated quasi-metric spaces. Second, we present a characterization of a unique fixed point for any mapping. Third, we prove another fixed point theorem in complete dislocated quasi-metric spaces. These theorems generalize known results, especially some theorems in [1–3, 5, 7, 8, 11–14, 16, 19, 20, 22]. Also, we give some comments on [17, Theorem 3] and [21, Theorem 1].

scholarly journals Unification of the Fixed Point in Integral Type Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 732 ◽  
Author(s):  
Panda Kumari ◽  
Badriah Alamri ◽  
Nawab Hussain ◽  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integral Type ◽  
Predominant Role

In metric fixed point theory, the conditions like “symmetry” and “triangle inequality” play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary.

scholarly journals Fixed Points Results in G-Metric Spaces

2019 ◽  
Vol 32 (1) ◽  
pp. 142
Author(s):  
Salwa Salman Abed ◽  
Anaam Neamah Faraj ◽  
Anaam Neamah Faraj
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Closed Ball ◽  
Local Contraction

  In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

scholarly journals Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 58 ◽  
Author(s):  
Ovidiu Popescu ◽  
Gabriel Stan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
The Self ◽  
Complete Metric Spaces

In this paper, we generalize some results of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), Cosentino and Vetro (Filomat 28:4, 2014), and Piri and Kumam (Fixed Point Theory Appl. 2014:210, 2014) theories by applying some weaker symmetrical conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.

scholarly journals Some fixed point theorems

1992 ◽  
Vol 53 (3) ◽  
pp. 304-312 ◽  
Author(s):  
P. V. Subrahmanyam ◽  
I. L. Reilly
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contraction Principle ◽  
Carry Over ◽  
Banach's Theorem ◽  
Banach’S Contraction Principle

AbstractBanach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.

scholarly journals The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with -Distances

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hossein Lakzian ◽  
Ing-Jer Lin
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Maps

Some fixed point theorems for -contractive maps and -contractive maps on a complete metric space are proved. Presented fixed point theorems generalize many results existing in the literature.

scholarly journals Applications of Fixed Point Theory in Integral Equations and Homotopy Using Partially Ordered S_b Metric Spaces

2018 ◽  
Vol 7 (3.3) ◽  
pp. 146 ◽  
Author(s):  
D Ram Prasad ◽  
GNV Kishore ◽  
K Priyanka
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Homotopy Theory ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Partially Ordered

In this paper we give some applications to integral equations as well as homotopy theory via Suzuki  type fixed point theorems in partially ordered complete  - metric space by using generalized contractive conditions. We also furnish an example which supports our main result.  

scholarly journals Common fixed point theorems for semigroups on metric spaces

1999 ◽  
Vol 22 (2) ◽  
pp. 377-386 ◽  
Author(s):  
Young-Ye Huang ◽  
Chung-Chien Hong
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Common Fixed Point Theorems ◽  
Lipschitzian Semigroup ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

This paper consists of two main results. The first one shows that ifSis a left reversible semigroup of selfmaps on a complete metric space(M,d)such that there is a gauge functionφfor whichd(f(x),f(y))≤φ(δ(Of (x,y)))forf∈Sandx,yinM, whereδ(Of (x,y))denotes the diameter of the orbit ofx,yunderf, thenShas a unique common fixed pointξinMand, moreover, for anyfinSandxinM, the sequence of iterates{fn(x)}converges toξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space(M,d).

Fixed point theorems in generalized metric spaces

2016 ◽  
Vol 10 (02) ◽  
pp. 1750030
Author(s):  
Stefan Czerwik ◽  
Krzysztof Król
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Banach Fixed Point Theorem ◽  
Generalized Metric Space ◽  
Generalized Metric

In the paper, we shall prove the results on the existence of fixed points of mapping defined on generalized metric space satisfying a nonlinear contraction condition, which is a generalization of Diaz and Margolis theorem (see [A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968) 305–309]). We also present local fixed point theorems both in generalized and ordinary metric spaces. Our results are generalizations of Banach fixed point theorem and many other results.

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