Uniform continuity of nonautonomous superposition operators in ΛBV-spaces

2019 ◽  
Vol 31 (3) ◽  
pp. 713-726
Author(s):  
Jacek Gulgowski
Keyword(s):  
Sufficient Conditions ◽  
Uniform Continuity ◽  
Regular Functions ◽  
Superposition Operators

Abstract In this paper we investigate the problem of uniform continuity of nonautonomous superposition operators acting between spaces of functions of bounded Λ-variation. In particular, we give the sufficient conditions for nonautonomous superposition operators to continuously map a space of functions of bounded Λ-variation into itself. The conditions cover the generators being functions of {C^{1}} -class (in view of two variables), but also allow for less regular functions, including discontinuous generators.

scholarly journals On equivalence of analytic functions to rational regular functions

1987 ◽  
Vol 43 (2) ◽  
pp. 279-286
Author(s):  
Wojciech Kucharz
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Regular Function ◽  
Sufficient Conditions ◽  
Regular Functions

AbstractWe give sufficient conditions for an analytic function from Rnto R to be analytically equivalent to a rational regular function.

scholarly journals Uniform continuity and Brézis–Lieb-type splitting for superposition operators in Sobolev space

2018 ◽  
Vol 7 (4) ◽  
pp. 587-599 ◽  
Author(s):  
Nils Ackermann
Keyword(s):  
Sobolev Space ◽  
Uniform Continuity ◽  
Independent Interest ◽  
Concentration Compactness ◽  
Intermediate Result ◽  
Superposition Operators ◽  
Compactness Arguments

AbstractUsing concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An intermediate result on the uniform continuity of superposition operators in Sobolev space is of independent interest.

DYNAMICAL PROPERTIES OF A STOCHASTIC TWO-SPECIES SCHOENER'S COMPETITIVE MODEL

2012 ◽  
Vol 05 (05) ◽  
pp. 1250035 ◽  
Author(s):  
JINGLIANG LV ◽  
KE WANG ◽  
MENG LIU
Keyword(s):  
Growth Rate ◽  
Positive Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Uniform Continuity ◽  
Stochastic Permanence ◽  
Sample Paths ◽  
Competitive Model ◽  
Dynamical Properties

A stochastic two-species Schoener's competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness, uniform continuity, global attractivity, stochastic permanence and extinction are obtained. Moreover, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.

scholarly journals Dynamics of an Impulsive Stochastic Predator–Prey System with the Beddington–DeAngelis Functional Response

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 323
Author(s):  
Yuanfu Shao
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Value Theory ◽  
Uniform Continuity ◽  
Quadratic Functions ◽  
Predator Prey ◽  
Prey System ◽  
Markovian Processes ◽  
Inequality Techniques

Taking impulsive effects into account, an impulsive stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, the impulsive system is transformed into an equivalent system without pulses. Then, by constructing suitable functionals and applying the extreme-value theory of quadratic functions, sufficient conditions on the existence of periodic Markovian processes are provided. The uniform continuity and global attractivity of solutions are also investigated. Additionally, we investigate the extinction and permanence in the mean of all species with the help of comparison methods and inequality techniques. Sufficient conditions on the existence and ergodicity of the stationary distribution of solutions for the autonomous and non-impulsive case are given. Finally, numerical simulations are performed to illustrate the main results.

scholarly journals On topological equivalence of R-uniformly continuous fuzzy metric spaces

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4523-4531
Author(s):  
Changqing Li ◽  
Yanlan Zhang ◽  
Jing Zhang
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Uniform Continuity ◽  
Fuzzy Metric Space ◽  
Topological Equivalence ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Necessary And Sufficient ◽  
Uniformly Continuous

The notion of uniform continuity in fuzzy metric spaces was first introduced by George and Veeramani in 1995. Later, Gregori et al. gave some contributions to the theory. As a consequence of the study, we introduce the notion of RUC fuzzy metric space. Also, necessary and sufficient conditions for a fuzzy metric space to be an RUC fuzzy metric space are studied. In addition, several examples are given.

scholarly journals Some sufficient conditions for univalence

1991 ◽  
Vol 14 (3) ◽  
pp. 619-623
Author(s):  
Sukhjit Singh
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Regular Functions

A new subclassR(α),0≤α≤1, of the classSt(1/2)the class of starlike functions of order1/2is introduced and it is shown thatR(α)is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit diskEare given.

scholarly journals Continuity of superposition operators on the double sequence spaces Lp

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2107-2118 ◽  
Author(s):  
Birsen Sağır ◽  
Nihan Güngör
Keyword(s):  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Superposition Operator ◽  
Double Sequence Spaces ◽  
Superposition Operators ◽  
Necessary And Sufficient

In this paper, we define the superposition operator Pg where g : N2 x R ? R by Pg((xks))=g(k,s,xks) for all real double sequence (xks). Chew & Lee [4] and Petranuarat & Kemprasit [7] have characterized Pg : lp ? l1 and Pg : lp ? lq where 1 ? p,q < ?, respectively. The main goal of this paper is to construct the necessary and sufficient conditions for the continuity of Pg: Lp ? L1 and Pg : Lp ? Lq where 1 ? p,q < ?.

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