Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
In this paper, we investigate various classes of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2825 |
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| author | Marko Kostić Wei-Shih Du Vladimir E. Fedorov |
| author_facet | Marko Kostić Wei-Shih Du Vladimir E. Fedorov |
| author_sort | Marko Kostić |
| collection | DOAJ |
| description | In this paper, we investigate various classes of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>:</mo><mi mathvariant="sans-serif">Λ</mi><mo>×</mo><mi>X</mi><mo>→</mo><mi>Y</mi><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∅</mo><mo>≠</mo><mi mathvariant="sans-serif">Λ</mi><mo>⊆</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>n</mi></msup><mo>,</mo></mrow></semantics></math></inline-formula><i> X</i> and <i>Y</i> are complex Banach spaces, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> is a binary relation on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo>.</mo></mrow></semantics></math></inline-formula> We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow></semantics></math></inline-formula>-periodic functions and Weyl-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given. |
| first_indexed | 2024-03-10T05:56:31Z |
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| id | doaj.art-1cfb2a52efde411cadce97ce5aca5998 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:56:31Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1cfb2a52efde411cadce97ce5aca59982023-11-22T21:19:23ZengMDPI AGMathematics2227-73902021-11-01921282510.3390/math9212825Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>Marko Kostić0Wei-Shih Du1Vladimir E. Fedorov2Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, SerbiaDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanMathematical Analysis Department, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, RussiaIn this paper, we investigate various classes of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>:</mo><mi mathvariant="sans-serif">Λ</mi><mo>×</mo><mi>X</mi><mo>→</mo><mi>Y</mi><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∅</mo><mo>≠</mo><mi mathvariant="sans-serif">Λ</mi><mo>⊆</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>n</mi></msup><mo>,</mo></mrow></semantics></math></inline-formula><i> X</i> and <i>Y</i> are complex Banach spaces, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> is a binary relation on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo>.</mo></mrow></semantics></math></inline-formula> We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow></semantics></math></inline-formula>-periodic functions and Weyl-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.https://www.mdpi.com/2227-7390/9/21/2825Doss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup>Lebesgue spaces with variable exponentsabstract Volterra integro-differential equations |
| spellingShingle | Marko Kostić Wei-Shih Du Vladimir E. Fedorov Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup> Mathematics Doss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup> Lebesgue spaces with variable exponents abstract Volterra integro-differential equations |
| title | Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup> |
| title_full | Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup> |
| title_fullStr | Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup> |
| title_full_unstemmed | Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup> |
| title_short | Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup> |
| title_sort | doss i ρ i almost periodic type functions in inline formula math display inline semantics mrow mi mathvariant double struck r mi mrow semantics math inline formula sup i n i sup |
| topic | Doss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup> Lebesgue spaces with variable exponents abstract Volterra integro-differential equations |
| url | https://www.mdpi.com/2227-7390/9/21/2825 |
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