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Pseudo asymptotically periodic mild solutions of semilinear functional integro‐differential equations in Banach spaces
Author(s) -
Xia Zhinan,
Wang Dingjiang,
Wen ChingFeng,
Yao JenChih
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4533
Subject(s) - mathematics , banach space , class (philosophy) , infinity , mathematical analysis , differential equation , c0 semigroup , pure mathematics , space (punctuation) , artificial intelligence , computer science , linguistics , philosophy
In this paper, we introduce and investigate the functions of ( μ , ν )‐pseudo S ‐asymptotically ω ‐periodic of class r (class infinity). We systematically explore the properties of these functions in Banach space including composition theorems. As applications, we establish some sufficient criteria for ( μ , ν )‐pseudo S ‐asymptotic ω ‐periodicity of (nonautonomous) semilinear integro‐differential equations with finite or infinite delay. Finally, some interesting examples are presented to illustrate the main findings.