scholarly journals On *-Continuity and *-Uniform Continuity of Some Non-Newtonian Superposition Operators

2021 ◽  
Author(s):  
Fatmanur ERDOGAN ◽  
Birsen SAĞIR DUYAR
Keyword(s):  
Uniform Continuity ◽  
Superposition Operators

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 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.

scholarly journals On Generalized Step-Functions and Superposition Operators

2004 ◽  
Vol 11 (4) ◽  
pp. 753-758
Author(s):  
A. Kharazishvili
Keyword(s):  
Step Functions ◽  
Functions Of Two Variables ◽  
Superposition Operators

Abstract For a given σ-ideal of sets, the notion of a generalized stepfunction is introduced and investigated in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators.

Uniform continuity of information combination

1992 ◽  
Vol 21 (5) ◽  
pp. 453-459 ◽  
Author(s):  
Beth Allen ◽  
Timothy Van Zandt
Keyword(s):  
Uniform Continuity

scholarly journals Multivalued function spaces and Atsuji spaces

2003 ◽  
Vol 4 (2) ◽  
pp. 201 ◽  
Author(s):  
Som Naimpally
Keyword(s):  
Uniform Continuity ◽  
Function Spaces ◽  
Multivalued Function ◽  
Vietoris Topology ◽  
Uniform Topology ◽  
Fell Topology

<p>In this paper we present two themes. The first one describes a transparent treatment of some of the recent results in graph topologies on multi-valued functions. The study includes Vietoris topology, Fell topology, Fell uniform topology on compacta and uniform topology on compacta. The second theme concerns when continuity is equivalent to proximal continuity or uniform continuity.</p>

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