scholarly journals On Stability of Fixed Points for Multi-Valued Mappings with an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qi-Qing Song
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Stable Fixed Point ◽  
Inclusion Problems ◽  
Point Mapping ◽  
Lower Semi ◽  
The Stability ◽  
Essential Sets ◽  
Almost All ◽  
Stable Result

This paper studies the stability of fixed points for multi-valued mappings in relation to selections. For multi-valued mappings admitting Michael selections, some examples are given to show that the fixed point mapping of these mappings are neither upper semi-continuous nor almost lower semi-continuous. Though the set of fixed points may be not compact for multi-valued mappings admitting Lipschitz selections, by finding sub-mappings of such mappings, the existence of minimal essential sets of fixed points is proved, and we show that there exists at least an essentially stable fixed point for almost all these mappings. As an application, we deduce an essentially stable result for differential inclusion problems.

scholarly journals Invariant curves around a parabolic fixed point at infinity

1990 ◽  
Vol 10 (2) ◽  
pp. 209-229 ◽  
Author(s):  
Dov Aharonov ◽  
Uri Elias
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Invariant Curves ◽  
The Stability ◽  
Area Preserving ◽  
Parabolic Fixed Point

AbstractThe stability of a fixed point of an area-preserving transformation in the plane is characterized by the invariant curves which surround it. The existence of invariant curves had been extensively studied for elliptic fixed points. Here we study the similar problem for parabolic fixed points. In particular we are interested in the case where the fixed point is at infinity.

New fixed point of on-orbit calibration scale based on the In-Bi eutectic alloy for application in novel high-stable space-borne standard sources

2021 ◽  
pp. 32-37
Author(s):  
Andrei A. Burdakin ◽  
Valerii R. Gavrilov ◽  
Ekaterina A. Us ◽  
Vitalii S. Bormashov
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Fixed Points ◽  
Eutectic Alloy ◽  
Earth Observation ◽  
Melt Temperature ◽  
Phase Transition Temperatures ◽  
Set Up ◽  
The Stability ◽  
Observation Space

The problem of ensuring stability of Earth observation space-borne instruments undertaking long-term temperature measurements within thermal IR spectral range is described. For in-flight reliable control of the space-borne IR instruments characteristics the stability of onboard reference sources should be improved. The function of these high-stable sources will be executed by novel onboard blackbodies, incorporating the melt↔freeze phase transition phenomenon, currently being developed. As a part of these works the task of realizing an on-orbit calibration scale within the dynamic temperature range of Earth observation systems 210−350 K based on fixed-point phase transition temperatures of a number of potentially suitable substances is advanced. The corresponding series of the onboard reference blackbodies will be set up on the basis of the on-orbit calibration scale fixed points. It is shown that the achievement of the target lies in carrying out a number of in-flight experiments with the selected fixed points and the prospective onboard fixed-point blackbodies prototypes. The new In-Bi eutectic alloy melt temperature fixed point (~345 K) is proposed as the significant fixed points of the future on-orbit calibration scale. The results of the new fixed point preliminary laboratory studies have been analyzed. The results allowed to start preparation of the in-flight experiments investigating the In-Bi alloy for the purpose of its application in the novel onboard reference sources.

scholarly journals Pattern Completion in Symmetric Threshold-Linear Networks

2016 ◽  
Vol 28 (12) ◽  
pp. 2825-2852 ◽  
Author(s):  
Carina Curto ◽  
Katherine Morrison
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Distance Geometry ◽  
Memory Encoding ◽  
Stable Fixed Point ◽  
Pattern Completion ◽  
Linear Networks ◽  
Firing Rate Models ◽  
Classical Distance ◽  
Symmetric Networks

Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically possess multiple stable fixed points (steady states), making them viable candidates for memory encoding and retrieval. In this work, we characterize stable fixed points of general threshold-linear networks with constant external drive and discover constraints on the coexistence of fixed points involving different subsets of active neurons. In the case of symmetric networks, we prove the following antichain property: if a set of neurons [Formula: see text] is the support of a stable fixed point, then no proper subset or superset of [Formula: see text] can support a stable fixed point. Symmetric threshold-linear networks thus appear to be well suited for pattern completion, since the dynamics are guaranteed not to get stuck in a subset or superset of a stored pattern. We also show that for any graph G, we can construct a network whose stable fixed points correspond precisely to the maximal cliques of G. As an application, we design network decoders for place field codes and demonstrate their efficacy for error correction and pattern completion. The proofs of our main results build on the theory of permitted sets in threshold-linear networks, including recently developed connections to classical distance geometry.

scholarly journals $$\alpha $$-Firmly nonexpansive operators on metric spaces

2022 ◽  
Vol 24 (1) ◽  
Author(s):  
Arian Bërdëllima ◽  
Florian Lauster ◽  
D. Russell Luke
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Metric Spaces ◽  
Uniformly Convex ◽  
Point Mapping ◽  
Splitting Algorithms ◽  
Uniformly Convex Spaces ◽  
Cluster Points ◽  
Convex Spaces

AbstractWe extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

scholarly journals Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Parin Chaipunya ◽  
Chirasak Mongkolkeha ◽  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Modular Metric Spaces ◽  
Contraction Type ◽  
The Stability

We give some initial properties of a subset of modular metric spaces and introduce some fixed-point theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals TARGET SPACE DUALITY AND MODULI STABILIZATION IN STRING GAS COSMOLOGY

2007 ◽  
Vol 22 (01) ◽  
pp. 165-179 ◽  
Author(s):  
AUTTAKIT CHATRABHUTI
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Moduli Space ◽  
Target Space ◽  
Moduli Stabilization ◽  
String Gas Cosmology ◽  
The Stability

Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

scholarly journals Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cemil Tunç ◽  
Emel Biçer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Differential Equations ◽  
Multiple Delays ◽  
Stability Of Solutions ◽  
Variable Delays ◽  
Multiple Variable ◽  
Fixed Point Technique ◽  
Functional Differential ◽  
The Stability

We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.

scholarly journals Stability of the Discrete Stage–Structure Prey–Predator Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Rehab Noori Shalan ◽  
Shireen R. Jawad ◽  
Alaa Hussien Lafta
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Three Dimensional ◽  
Stage Structure ◽  
Prey Population ◽  
Topological Properties ◽  
Proposed Model ◽  
Predator Model ◽  
The Stability ◽  
Theoretical Results

This paper discusses the discrete stage–structure prey-predator model involved in the Beddington–DeAngelis type of functional response described by differential equation systems proposed as three-dimensional systems. Furthermore, the predators are divided into two types of populations, namely, mature and immature, along with the prey population. The stability of all possible fixed points is demonstrated by solving our proposed model analytically using the standard lemma and topological properties, which give all possible properties to each fixed point. In the same manner, we identify three fixed points, which are as follows: the origin fixed point, which means there are no species; the axial fixed point, which means the prey population increases logistically with the absence of a predator one (mature and immature populations); and the positive fixed point, which signifies the coexistence of all species. We show that the numerical simulations part is used not only to plot the time series of fixed values, but also, to find and illustrate the theoretical results.

scholarly journals Fixed point theorems on expansion type maps in intuitionistic fuzzy metric space

1970 ◽  
Vol 7 (1) ◽  
pp. 38-47
Author(s):  
MS Chauhan ◽  
Bijendra Singh ◽  
Bharat Singh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fuzzy Sets ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
Type Mapping ◽  
Intuitionistic Fuzzy ◽  
Almost All

Ever since the introduction of fuzzy sets by Zadeh [1] , the fuzzyness invaded almost all the branches of crisp mathematics. Deng [3] kaleva and Seikalla [2] and Kramosil and Michalek [5]Have introduced the concept of fuzzy metric space, George and Veeramani [4] modified the concept of fuzzy metric space introduced by kramosil and michalek [5]. In thia paper effort has been made to obtain some results on fixed points of expansion type mapping in Intuitionistic fuzzy metric space DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5420 KUSET 2011; 7(1): 38-47

Sign in / Sign up

Export Citation Format

Share Document