Description

• Title:
  Remarks connected with the weak limit of iterates of some random-valued functions and iterative functional equations
• Creator:
  Baron, Karol
• Description:
  The paper consists of two parts. At first, assuming that (Ω,𝒜,P) is a probability space and (X,ρ) is a complete and separable metric space with the σ-algebra 𝐵 of all its Borel subsets we consider the set 𝑅c of all 𝐵⊗𝒜 measurable and contractive in mean functions f:X×Ω→X with finite integral ∫Ωρ(f(x,ω),x)P(dω) for x∈X, the weak limit πf of the sequence of iterates of f∈𝑅c, and investigate continuity-like property of the function f↦πf, f∈𝑅c, and Lipschitz solutions ϕ that take values in a separable Banach space of the equationϕ(x) = ∫Ωϕ(f(x,ω))P(dω) + F(x).Next, assuming that X is a real separable Hilbert space, Λ:X→X is linear and continuous with ‖Λ‖<1, and μ is a probability Borel measure on X with finite first moment we examine continuous at zero solutions ϕ:X→ℂ of the equationϕ(x) = μ^(x)ϕ(Λx)which characterizes the limit distribution πf for some special f∈𝑅c.
• Object availability:
  free access
• Date:
  2020.05.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol 34 No 1 (2020); 36-44;
  Annales Mathematicae Silesianae; Tom 34 Nr 1 (2020); 36-44;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/13629/10436
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/13629
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other