Some characterizations of the topology of uniform convergence on order-bounded sets

1976 ◽  
pp. 104-155
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Uniform Convergence ◽  
Bounded Sets

scholarly journals Generic well-posedness in minimization problems

2005 ◽  
Vol 2005 (4) ◽  
pp. 343-360 ◽  
Author(s):  
A. Ioffe ◽  
R. E. Lucchetti
Keyword(s):  
Uniform Convergence ◽  
Well Posedness ◽  
Minimization Problems ◽  
Bounded Sets ◽  
Well Posed ◽  
Class Of Functions

The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bounded sets, or similar convergence notions, as far as the topology on the class of functions under investigation is concerned.

scholarly journals A nonlinear version of Halanay's inequality for the uniform convergence to the origin

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pierdomenico Pepe
Keyword(s):  
Uniform Convergence ◽  
Functional Differential Equations ◽  
Lyapunov Methods ◽  
Uniform Asymptotic Stability ◽  
Retarded Functional Differential Equations ◽  
Nonlinear Version ◽  
Halanay’S Inequality ◽  
Functional Differential ◽  
The Relationship ◽  
Bounded Sets

<p style='text-indent:20px;'>A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.</p>

QUASI-UNIFORM CONVERGENCE AND ℒ-SPACES

1992 ◽  
Vol 18 (2) ◽  
pp. 321 ◽  
Author(s):  
Bukovská ◽  
Bukovský ◽  
Ewert
Keyword(s):  
Uniform Convergence

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

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