Search results for "fixed"
showing 10 items of 639 documents
Fixed point theorems for multivalued maps via new auxiliary function
2016
We introduce a contractive condition involving new auxiliary function and prove a fixed point theorem for closed multivalued maps on complete metric spaces. An example and an application to integral equation are given in support of our findings.
Existence of fixed points and measures of weak noncompactness
2009
Abstract The purpose of this paper is to study the existence of fixed points by using measures of weak noncompactness. Later on, we provide an existence principle for solutions for a nonlinear integral equation.
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations
2012
In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.
Coincidence problems for generalized contractions
2014
In this paper, we establish some new existence, uniqueness and Ulam-Hyers stability theorems for coincidence problems for two single-valued mappings. The main results of this paper extend the results presented in O. Mle?ni?e: Existence and Ulam-Hyers stability results for coincidence problems, J. Non-linear Sci. Appl., 6(2013), 108-116. In the last section two examples of application of these results are also given.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
Convergence of KAM iterations for counterterm problems
1998
Abstract We analyse two iterative KAM methods for counterterm problems for finite-dimensional matrices. The starting point for these methods is the KAM iteration for Hamiltonians linear in the action variable in classical mechanics. We compare their convergence properties when a perturbation parameter is varied. The first method has no fixed points beyond a critical value of the perturbation parameter. The second one has fixed points for arbitrarily large perturbations. We observe different domains of attraction separated by Julia sets.
Attractors/Basin of Attraction
2020
It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term …
Über die Autoxydation ungesättigter Verbindungen VIII. Mitteilung. Eine Methode zur erfassung des anfangsverlaufs der Autoxydation
1959
Es wird eine Methods beschrieben, die den Anfangsverlauf der Autoxydation von substanzen mit niedrigem Dampfdruck (Linolsauremethylester) manometrisch zu verfolgen gestattet. Die Reaktionsgefase sind mit einer Ampullenzertrummerungsvorrichtung ausgestattet, so das die Substanz erst zu einem genau festgelegten Zeitpunkt mit Sauerstoff in Beruhrung gebracht werden kann. Es ist so moglich, die Lolichkeit des Sauerstoffs in der Substanz zu bestimmen. A method is described which measures manometrically the beginning of the autoxidation of substances of low vapour pressure (methyllinoleate). The reaction vessela are fitted out with an equipment to break the ampoules, so that the substance can be …
Fluorescence In Situ Hybridization (FISH) on Formalin-Fixed Paraffin-Embedded (FFPE) Tissue Sections
2011
Fluorescence In Situ Hybridization (FISH) is a powerful technique for localizing specific DNA targets directly in the fixed tissue or cells. Bacterial artificial chromosome (BAC) as well as commercial probes, which could be supplied ready for use or concentrated and must be diluted following the manufacturers instructions, can be used. The technique requires 2 days, as an overnight incubation of the FISH probes is needed for optimal hybridization. The critical steps include deparaffinization of tissue sections, optimal pretreatment (target retrieval and protein digestion), and probe hybridization. In this chapter, the described FISH protocol provides a methodology for analyzing the cytogene…
MR3098564 Reviewed Al-Thagafi, M. A.; Shahzad, Naseer Krasnosel'skii-type fixed-point results. J. Nonlinear Convex Anal. 14 (2013), no. 3, 483–491. (…
2014
The Krasnosel'skii fixed-point theorem is a powerful tool in dealing with various types of integro-differential equations. The initial motivation of this theorem is the fact that the inversion of a perturbed differential operator may yield the sum of a continuous compact mapping and a contraction mapping. Following and improving this idea, many fixed-point results were proved.\\ The authors present significant and interesting contributions in this direction. In particular, they give the following main theorem: \begin{theorem} Let $M$ be a nonempty bounded closed convex subset of a Banach space $E$, $S:M \to E$ and $T:M \to E$. Suppose that \begin{itemize} \item[(a)] $S$ is 1-set-contractive…