Note on an Iterative Functional Equation
We study the problem of solvability of the equation ϕ(x)=∫Ωg(w)ϕ(f(x,ω))P(dω)+F(x),\varphi \left( x \right) = \int_\Omega {g\left( w \right)} \varphi \left( {f\left( {x,\omega } \right)} \right)P\left( {d\omega } \right) + F\left( x \right), where P is a probability measure on a σ-algebra of subset...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2024-03-01
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| Series: | Annales Mathematicae Silesianae |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amsil-2023-0031 |
| _version_ | 1827298422568255488 |
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| author | Baron Karol Morawiec Janusz |
| author_facet | Baron Karol Morawiec Janusz |
| author_sort | Baron Karol |
| collection | DOAJ |
| description | We study the problem of solvability of the equation
ϕ(x)=∫Ωg(w)ϕ(f(x,ω))P(dω)+F(x),\varphi \left( x \right) = \int_\Omega {g\left( w \right)} \varphi \left( {f\left( {x,\omega } \right)} \right)P\left( {d\omega } \right) + F\left( x \right),
where P is a probability measure on a σ-algebra of subsets of Ω, assuming Hölder continuity of F on the range of f. |
| first_indexed | 2024-04-24T15:14:36Z |
| format | Article |
| id | doaj.art-1fb5f51bf6d649c99a5e5649943b41dc |
| institution | Directory Open Access Journal |
| issn | 2391-4238 |
| language | English |
| last_indexed | 2024-04-24T15:14:36Z |
| publishDate | 2024-03-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Mathematicae Silesianae |
| spelling | doaj.art-1fb5f51bf6d649c99a5e5649943b41dc2024-04-02T09:28:47ZengSciendoAnnales Mathematicae Silesianae2391-42382024-03-01381121710.2478/amsil-2023-0031Note on an Iterative Functional EquationBaron Karol0Morawiec Janusz11Institute of Mathematics, University of Silesia, Bankowa 14, PL-40-007Katowice, Poland1Institute of Mathematics, University of Silesia, Bankowa 14, PL-40-007Katowice, PolandWe study the problem of solvability of the equation ϕ(x)=∫Ωg(w)ϕ(f(x,ω))P(dω)+F(x),\varphi \left( x \right) = \int_\Omega {g\left( w \right)} \varphi \left( {f\left( {x,\omega } \right)} \right)P\left( {d\omega } \right) + F\left( x \right), where P is a probability measure on a σ-algebra of subsets of Ω, assuming Hölder continuity of F on the range of f.https://doi.org/10.2478/amsil-2023-0031iterative functional equationshölder continuous functions39b12 |
| spellingShingle | Baron Karol Morawiec Janusz Note on an Iterative Functional Equation Annales Mathematicae Silesianae iterative functional equations hölder continuous functions 39b12 |
| title | Note on an Iterative Functional Equation |
| title_full | Note on an Iterative Functional Equation |
| title_fullStr | Note on an Iterative Functional Equation |
| title_full_unstemmed | Note on an Iterative Functional Equation |
| title_short | Note on an Iterative Functional Equation |
| title_sort | note on an iterative functional equation |
| topic | iterative functional equations hölder continuous functions 39b12 |
| url | https://doi.org/10.2478/amsil-2023-0031 |
| work_keys_str_mv | AT baronkarol noteonaniterativefunctionalequation AT morawiecjanusz noteonaniterativefunctionalequation |