Existence and stability of the solution of an implicit set-valued functional differential equation with parameters | ||
| Electronic Journal of Mathematical Analysis and Applications | ||
| Article 3, Volume 13, Issue 2, 2025, Pages 1-7 PDF (391.84 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/ejmaa.2025.354162.1311 | ||
| Authors | ||
| sooma saad* 1; Fathi Emharab2 | ||
| 1رياضيات-جامعة عمر امختار | ||
| 2كلية تربية-قسم رياضيات-جامعة عمر المختار | ||
| Abstract | ||
| A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory. The set-valued functional differential equation has been widely applied in mathematics, physics, optimizations, optimal control, as well as economics and finance.[2, 3, 5, 6]. Here, we study the initial-value problem of a set-valued implicate functional differential equation with parameters. The existence of solution and its continuous dependence on parameters will be proved we study the existence of solutions of the parametric set-valued implicit functional differential equation The existence of solutions x ∈ C[0, T], C[0, T] is the Banach space of continuous functions defined on [0, T], will be proved. The continuous dependence of the solutions on the initial value x0 and the parameters γ. µ will be proved also. | ||
| Keywords | ||
| plied in mathematics; physics; optimizations; optimal control; as well as economics and finance | ||
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