A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument
This work is mainly focused on square-mean <i>S</i>-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean <i>S</i>-asymptotically Bloch type periodic processes with values in complex Hilbert spaces...
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/9/1495 |
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| author | Mamadou Moustapha Mbaye Amadou Diop Gaston Mandata N’Guérékata |
| author_facet | Mamadou Moustapha Mbaye Amadou Diop Gaston Mandata N’Guérékata |
| author_sort | Mamadou Moustapha Mbaye |
| collection | DOAJ |
| description | This work is mainly focused on square-mean <i>S</i>-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean <i>S</i>-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze some qualitative properties of this type of processes. These properties, combined with the inequality technique, evolution operator theory, fixed-point theory, and stochastic analysis approach, allow us to establish conditions for the existence and uniqueness of square-mean <i>S</i>-asymptotically Bloch type periodicity of bounded mild solutions for a class of stochastic evolution equations with infinite delay and piecewise constant argument. In the end, examples are given to illustrate the feasibility of our results. |
| format | Article |
| id | doaj-art-d28fea959ae747bbb15d142ed872ddcb |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d28fea959ae747bbb15d142ed872ddcb2025-08-20T01:49:28ZengMDPI AGMathematics2227-73902025-04-01139149510.3390/math13091495A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant ArgumentMamadou Moustapha Mbaye0Amadou Diop1Gaston Mandata N’Guérékata2Laboratoire de Mathématiques Appliquées (LMA), Département de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Fann, Dakar BP 5005, SenegalClasses Préparatoires aux Grandes Écoles (CPGE), Thiès BP A10, SenegalNEERLab, Department of Mathematics, Morgan State University, Baltimore, MD 21251, USAThis work is mainly focused on square-mean <i>S</i>-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean <i>S</i>-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze some qualitative properties of this type of processes. These properties, combined with the inequality technique, evolution operator theory, fixed-point theory, and stochastic analysis approach, allow us to establish conditions for the existence and uniqueness of square-mean <i>S</i>-asymptotically Bloch type periodicity of bounded mild solutions for a class of stochastic evolution equations with infinite delay and piecewise constant argument. In the end, examples are given to illustrate the feasibility of our results.https://www.mdpi.com/2227-7390/13/9/1495stochastic processesstochastic evolution equationspseudo-S-asymptotically Bloch type periodic functions |
| spellingShingle | Mamadou Moustapha Mbaye Amadou Diop Gaston Mandata N’Guérékata A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument Mathematics stochastic processes stochastic evolution equations pseudo-S-asymptotically Bloch type periodic functions |
| title | A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument |
| title_full | A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument |
| title_fullStr | A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument |
| title_full_unstemmed | A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument |
| title_short | A Study on Square-Mean <i>S</i>-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument |
| title_sort | study on square mean i s i asymptotically bloch type periodic solutions for some stochastic evolution systems with piecewise constant argument |
| topic | stochastic processes stochastic evolution equations pseudo-S-asymptotically Bloch type periodic functions |
| url | https://www.mdpi.com/2227-7390/13/9/1495 |
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