Generalized <i>ρ</i>-Almost Periodic Sequences and Applications
In this paper, we analyze the Bohr <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type sequences and the generalized <in...
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/5/410 |
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| author | Marko Kostić Belkacem Chaouchi Wei-Shih Du Daniel Velinov |
| author_facet | Marko Kostić Belkacem Chaouchi Wei-Shih Du Daniel Velinov |
| author_sort | Marko Kostić |
| collection | DOAJ |
| description | In this paper, we analyze the Bohr <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type sequences and the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type sequences of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>:</mo><mi>I</mi><mo>×</mo><mi>X</mi><mo>→</mo><mi>Y</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∅</mo><mo>≠</mo><mi>I</mi><mo>⊆</mo><msup><mrow><mi mathvariant="double-struck">Z</mi></mrow><mi>n</mi></msup></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 general 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 provide many structural results, observations and open problems about the introduced classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic sequences. Certain applications of the established theoretical results to the abstract Volterra integro-difference equations are also given. |
| first_indexed | 2024-03-11T03:42:56Z |
| format | Article |
| id | doaj.art-b35850204aed4d8d9ee4f05a194e4f6f |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:42:56Z |
| publishDate | 2023-05-01 |
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| series | Fractal and Fractional |
| spelling | doaj.art-b35850204aed4d8d9ee4f05a194e4f6f2023-11-18T01:26:44ZengMDPI AGFractal and Fractional2504-31102023-05-017541010.3390/fractalfract7050410Generalized <i>ρ</i>-Almost Periodic Sequences and ApplicationsMarko Kostić0Belkacem Chaouchi1Wei-Shih Du2Daniel Velinov3Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, SerbiaLaboratory de l’Energie et des Systèmes Intelligents, Khemis Miliana University, Khemis Miliana 44225, AlgeriaDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanDepartment 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 analyze the Bohr <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type sequences and the generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type sequences of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>:</mo><mi>I</mi><mo>×</mo><mi>X</mi><mo>→</mo><mi>Y</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∅</mo><mo>≠</mo><mi>I</mi><mo>⊆</mo><msup><mrow><mi mathvariant="double-struck">Z</mi></mrow><mi>n</mi></msup></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 general 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 provide many structural results, observations and open problems about the introduced classes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic sequences. Certain applications of the established theoretical results to the abstract Volterra integro-difference equations are also given.https://www.mdpi.com/2504-3110/7/5/410generalized <i>ρ</i>-almost periodic sequencegeneralized <i>ρ</i>-almost periodic functionabstract Volterra integro-difference equationabstract impulsive Volterra integro-differential equationBanach space |
| spellingShingle | Marko Kostić Belkacem Chaouchi Wei-Shih Du Daniel Velinov Generalized <i>ρ</i>-Almost Periodic Sequences and Applications Fractal and Fractional generalized <i>ρ</i>-almost periodic sequence generalized <i>ρ</i>-almost periodic function abstract Volterra integro-difference equation abstract impulsive Volterra integro-differential equation Banach space |
| title | Generalized <i>ρ</i>-Almost Periodic Sequences and Applications |
| title_full | Generalized <i>ρ</i>-Almost Periodic Sequences and Applications |
| title_fullStr | Generalized <i>ρ</i>-Almost Periodic Sequences and Applications |
| title_full_unstemmed | Generalized <i>ρ</i>-Almost Periodic Sequences and Applications |
| title_short | Generalized <i>ρ</i>-Almost Periodic Sequences and Applications |
| title_sort | generalized i ρ i almost periodic sequences and applications |
| topic | generalized <i>ρ</i>-almost periodic sequence generalized <i>ρ</i>-almost periodic function abstract Volterra integro-difference equation abstract impulsive Volterra integro-differential equation Banach space |
| url | https://www.mdpi.com/2504-3110/7/5/410 |
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