scholarly journals A fixed point theorem for Boolean networks expressed in terms of forbidden subnetworks

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Adrien Richard
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Adjacency Matrix ◽  
Jacobian Matrix ◽  
Unique Fixed Point ◽  
Boolean Networks ◽  
Directed Cycle ◽  
Interaction Graph ◽  
International Audience

International audience We are interested in fixed points in Boolean networks, $\textit{i.e.}$ functions $f$ from $\{0,1\}^n$ to itself. We define the subnetworks of $f$ as the restrictions of $f$ to the hypercubes contained in $\{0,1\}^n$, and we exhibit a class $\mathcal{F}$ of Boolean networks, called even or odd self-dual networks, satisfying the following property: if a network $f$ has no subnetwork in $\mathcal{F}$, then it has a unique fixed point. We then discuss this "forbidden subnetworks theorem''. We show that it generalizes the following fixed point theorem of Shih and Dong: if, for every $x$ in $\{0,1\}^n$, there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of $f$ evaluated at point $x$, then $f$ has a unique fixed point. We also show that $\mathcal{F}$ contains the class $\mathcal{F'}$ of networks whose the interaction graph is a directed cycle, but that the absence of subnetwork in $\mathcal{F'}$ does not imply the existence and the uniqueness of a fixed point.

scholarly journals A Fixed-Point Theorem for Ordered Contraction-Type Decreasing Operators in Banach Space with Lattice Structure

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Chenguang Wang ◽  
Jinxiu Mao ◽  
Zengqin Zhao
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Iterative Algorithm ◽  
Point Theorem ◽  
Unique Fixed Point ◽  
Lattice Structure ◽  
Contraction Type

In this work, we mainly improve the results in Amini-Harandi and Emami (2010). By introducing a new kind of ordered contraction-type decreasing operator in Banach space, we obtain a unique fixed point by using the iterative algorithm. An example is also presented to illustrate the theorem.

scholarly journals Fixed Point Results Satisfying Rational Type Contraction inG-Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Branislav Z. Popović ◽  
Muhammad Shoaib ◽  
Muhammad Sarwar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Rational Type ◽  
Type Contraction

A unique fixed point theorem for three self-maps under rational type contractive condition is established. In addition, a unique fixed point result for six continuous self-mappings through rational type expression is also discussed.

scholarly journals A remark on Rhoades fixed point theorem for non-self mappings

1993 ◽  
Vol 16 (2) ◽  
pp. 397-400 ◽  
Author(s):  
Ljubomir B. ciric
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Closed Subset ◽  
Unique Fixed Point

LetXbe a Banach space,Ka non-empty closed subset ofXandT:K→Xa mapping satisfying the contractive definition (1.1) below and the conditionT(∂K)⫅K. ThenThas a unique fixed point inK. This result improves Theorem of Rhoades [1] and generalizes the corresponding theorem of Assad [2].

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 Fixed point theorem with contractive mapping on C*-Algebra valued G-Metric Space

2021 ◽  
Vol 2106 (1) ◽  
pp. 012015
Author(s):  
A Wijaya ◽  
N Hariadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contractive Mapping ◽  
C Algebra ◽  
Metric Function ◽  
Interesting Theorem

Abstract Banach-Caccioppoli Fixed Point Theorem is an interesting theorem in metric space theory. This theorem states that if T : X → X is a contractive mapping on complete metric space, then T has a unique fixed point. In 2018, the notion of C *-algebra valued G-metric space was introduced by Congcong Shen, Lining Jiang, and Zhenhua Ma. The C *-algebra valued G-metric space is a generalization of the G-metric space and the C*-algebra valued metric space, meanwhile the G-metric space and the C *-algebra valued metric space itself is a generalization of known metric space. The G-metric generalized the domain of metric from X × X into X × X × X, the C *-algebra valued metric generalized the codomain from real number into C *-algebra, and the C *-algebra valued G-metric space generalized both the domain and the codomain. In C *-algebra valued G-metric space, there is one theorem that is similar to the Banach-Caccioppoli Fixed Point Theorem, called by fixed point theorem with contractive mapping on C *-algebra valued G-metric space. This theorem is already proven by Congcong Shen, Lining Jiang, Zhenhua Ma (2018). In this paper, we discuss another new proof of this theorem by using the metric function d(x, y) = max{G(x, x, y),G(y, x, x)}.

scholarly journals A fixed point theorem with applications to convolution equations

1963 ◽  
Vol 3 (4) ◽  
pp. 385-395 ◽  
Author(s):  
R. E. Edwards
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Banach Contraction Principle ◽  
Banach Contraction ◽  
Image Position ◽  
Convolution Equations

The well-known Banach Contraction Principle asserts that any self-map F of a complete metric space M with the property that, for some number k < 1, for all x, y,∈M, possesses a unique fixed point in M. some extensions and analogues have recently been given by Edelstein [1]. For the reader's convenlience we state here the result of Edelstein which we shall employ. It asserts that if F is a self-map of a metric space M having the property that for any two distinct points x and y of M, and if x0 is a point of M such that the sequence of iterates xn = Fn (x0) contains a subsequence which converges in M, then the limit of this subsequence is the unique fixed point of F.

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