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A Study on Square-Mean S -Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

Author

Listed:
  • Mamadou Moustapha Mbaye

    (Laboratoire de Mathématiques Appliquées (LMA), Département de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Fann, Dakar BP 5005, Senegal)

  • Amadou Diop

    (Classes Préparatoires aux Grandes Écoles (CPGE), Thiès BP A10, Senegal
    Laboratoire d’Analyse Numérique et Informatique, Université Gaston Berger, Saint-Louis BP 234, Senegal)

  • Gaston Mandata N’Guérékata

    (NEERLab, Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA)

Abstract

This work is mainly focused on square-mean S -asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean S -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 S -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.

Suggested Citation

  • Mamadou Moustapha Mbaye & Amadou Diop & Gaston Mandata N’Guérékata, 2025. "A Study on Square-Mean S -Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument," Mathematics, MDPI, vol. 13(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1495-:d:1647172
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