The superposition operator in the space of functions continuous and converging at infinity on the real half-axis

Advances in Nonlinear Analysis

article

Beata Rzepka¹  Justyna Ścibisz¹ 

[1] Department of Nonlinear Analysis, Rzeszów University of Technology

关键词: Banach space;    space of functions defined;    continuous on the half-axis and converging at infinity;    superposition operator;    Cauchy condition at infinity;    equicontinuous functions;    relatively compact set;   

DOI  :  10.1515/anona-2020-0046

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We will consider the so-called superposition operator in the space CC (ℝ + ) of real functions defined, continuous on the real half-axis ℝ + and converging to finite limits at infinity. We will assume that the function f = f ( t , x ) generating the mentioned superposition operator is locally uniformly continuous with respect to the variable x uniformly for t ∈ ℝ + . Moreover, we require that the function t → f ( t , x ) satisfies the Cauchy condition at infinity uniformly with respect to the variable x . Under the above indicated assumptions a few properties of the superposition operator in question are derived. Examples illustrating our considerations will be included.

【 授权许可】

CC BY