Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions
In this paper, we introduce and systematically analyze the classes of (pre-)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">B</mi><mo...
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/2/147 |
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| author | Wei-Shih Du Marko Kostić Daniel Velinov |
| author_facet | Wei-Shih Du Marko Kostić Daniel Velinov |
| author_sort | Wei-Shih Du |
| collection | DOAJ |
| description | In this paper, we introduce and systematically analyze the classes of (pre-)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">B</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mrow><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></semantics></math></inline-formula>-piecewise continuous almost periodic functions and (pre-)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">B</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mrow><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></semantics></math></inline-formula>-piecewise continuous uniformly recurrent functions with values in complex Banach spaces. We weaken substantially, or remove completely, the assumption that the sequence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> of possible first kind discontinuities of the function under consideration is a Wexler sequence (in order to achieve these aims, we use certain results about Stepanov almost periodic type functions). We provide many applications in the analysis of the existence and uniqueness of almost periodic type solutions for various classes of the abstract impulsive Volterra integro-differential inclusions. |
| first_indexed | 2024-03-11T08:48:55Z |
| format | Article |
| id | doaj.art-7a76f3544653426283b6268151f39a0a |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T08:48:55Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-7a76f3544653426283b6268151f39a0a2023-11-16T20:36:38ZengMDPI AGFractal and Fractional2504-31102023-02-017214710.3390/fractalfract7020147Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential InclusionsWei-Shih Du0Marko Kostić1Daniel Velinov2Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanFaculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, SerbiaDepartment for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje, Partizanski Odredi 24, P.O. Box 560, 1000 Skopje, North MacedoniaIn this paper, we introduce and systematically analyze the classes of (pre-)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">B</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mrow><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></semantics></math></inline-formula>-piecewise continuous almost periodic functions and (pre-)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">B</mi><mo>,</mo><mi>ρ</mi><mo>,</mo><mrow><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>)</mo></mrow><mo>)</mo></mrow></semantics></math></inline-formula>-piecewise continuous uniformly recurrent functions with values in complex Banach spaces. We weaken substantially, or remove completely, the assumption that the sequence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>t</mi><mi>k</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> of possible first kind discontinuities of the function under consideration is a Wexler sequence (in order to achieve these aims, we use certain results about Stepanov almost periodic type functions). We provide many applications in the analysis of the existence and uniqueness of almost periodic type solutions for various classes of the abstract impulsive Volterra integro-differential inclusions.https://www.mdpi.com/2504-3110/7/2/147(<i>ℬ</i>,<i>ρ</i>,(<i>t<sub>k</sub></i>))-piecewise continuous almost periodic type functions(<i>ℬ</i>,<i>ρ</i>,(<i>t<sub>k</sub></i>))-piecewise continuous uniformly recurrent type functionsWexler sequencesabstract impulsive Volterra integro-differential inclusionsalmost periodic type solutions |
| spellingShingle | Wei-Shih Du Marko Kostić Daniel Velinov Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions Fractal and Fractional (<i>ℬ</i>,<i>ρ</i>,(<i>t<sub>k</sub></i>))-piecewise continuous almost periodic type functions (<i>ℬ</i>,<i>ρ</i>,(<i>t<sub>k</sub></i>))-piecewise continuous uniformly recurrent type functions Wexler sequences abstract impulsive Volterra integro-differential inclusions almost periodic type solutions |
| title | Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions |
| title_full | Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions |
| title_fullStr | Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions |
| title_full_unstemmed | Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions |
| title_short | Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions |
| title_sort | almost periodic solutions of abstract impulsive volterra integro differential inclusions |
| topic | (<i>ℬ</i>,<i>ρ</i>,(<i>t<sub>k</sub></i>))-piecewise continuous almost periodic type functions (<i>ℬ</i>,<i>ρ</i>,(<i>t<sub>k</sub></i>))-piecewise continuous uniformly recurrent type functions Wexler sequences abstract impulsive Volterra integro-differential inclusions almost periodic type solutions |
| url | https://www.mdpi.com/2504-3110/7/2/147 |
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