Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations
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 of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in mean functions f : X × Ω → X with finite integ...
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| Format: | Article |
| Language: | English |
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Sciendo
2020-07-01
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| Series: | Annales Mathematicae Silesianae |
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| Online Access: | http://www.degruyter.com/view/j/amsil.2020.34.issue-1/amsil-2019-0015/amsil-2019-0015.xml?format=INT |
| _version_ | 1830516069783044096 |
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| author | Baron Karol |
| author_facet | Baron Karol |
| author_sort | Baron Karol |
| collection | DOAJ |
| 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 of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in mean functions f : X × Ω → X with finite integral ∫ Ω ϱ (f(x, ω), x) P (dω) for x ∈ X, the weak limit π f of the sequence of iterates of f ∈ c, and investigate continuity-like property of the function f ↦ πf, f ∈ c, and Lipschitz solutions φ that take values in a separable Banach space of the equation |
| first_indexed | 2024-12-22T03:34:25Z |
| format | Article |
| id | doaj.art-9b06e66cf10d4f60a21bfcf8f1b4c749 |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-12-22T03:34:25Z |
| publishDate | 2020-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-9b06e66cf10d4f60a21bfcf8f1b4c7492022-12-21T18:40:25ZengSciendoAnnales Mathematicae Silesianae2391-42382020-07-01341364410.2478/amsil-2019-0015amsil-2019-0015Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional EquationsBaron Karol0Institute of mathematics, University of Silesia, Bankowa 14, 40-007Katowice, PolandThe 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 of all its Borel subsets we consider the set c of all ⊗ 𝒜-measurable and contractive in mean functions f : X × Ω → X with finite integral ∫ Ω ϱ (f(x, ω), x) P (dω) for x ∈ X, the weak limit π f of the sequence of iterates of f ∈ c, and investigate continuity-like property of the function f ↦ πf, f ∈ c, and Lipschitz solutions φ that take values in a separable Banach space of the equationhttp://www.degruyter.com/view/j/amsil.2020.34.issue-1/amsil-2019-0015/amsil-2019-0015.xml?format=INTrandom-valued functionsiteratesconvergence in lawcontinuous dependence on the given functionfourier transformiterative functional equationscontinuous and lipschitz solutions26a1839b1239b3239b5260b1260b15 |
| spellingShingle | Baron Karol Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations Annales Mathematicae Silesianae random-valued functions iterates convergence in law continuous dependence on the given function fourier transform iterative functional equations continuous and lipschitz solutions 26a18 39b12 39b32 39b52 60b12 60b15 |
| title | Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations |
| title_full | Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations |
| title_fullStr | Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations |
| title_full_unstemmed | Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations |
| title_short | Remarks Connected with the Weak Limit of Iterates of Some Random-Valued Functions and Iterative Functional Equations |
| title_sort | remarks connected with the weak limit of iterates of some random valued functions and iterative functional equations |
| topic | random-valued functions iterates convergence in law continuous dependence on the given function fourier transform iterative functional equations continuous and lipschitz solutions 26a18 39b12 39b32 39b52 60b12 60b15 |
| url | http://www.degruyter.com/view/j/amsil.2020.34.issue-1/amsil-2019-0015/amsil-2019-0015.xml?format=INT |
| work_keys_str_mv | AT baronkarol remarksconnectedwiththeweaklimitofiteratesofsomerandomvaluedfunctionsanditerativefunctionalequations |