Stability and Continuous Dependence of the Solution of a Set-Valued Functional Equation with the Parameter

Somyya Amrajaa; Imparak Sulayman; Abdulbari Jawwad

doi:10.54361/ajmas.2691003

Stability and Continuous Dependence of the Solution of a Set-Valued Functional Equation with the Parameter

Authors

Somyya Amrajaa Faculty of Science, Omar al Mukhtar University, Libya https://orcid.org/0000-0003-1268-8976
Imparak Sulayman Faculty of Science, Omar al Mukhtar University, Libya https://orcid.org/0000-0002-9046-7741
Abdulbari Jawwad Faculty of Science, the Islamic University of Mohamed Bin Ali Al Sanussi, Libya https://orcid.org/0000-0002-2377-2105

DOI:

https://doi.org/10.54361/ajmas.2691003

Keywords:

A Set-Valued Functional Equation: Lipschitz Condition: Banach Space

Abstract

In this paper, we study the existence and stability of the Set-Valued functional equation with a parameter in x ∈ L₁[0, T].[1, 5, 12]. The existence of solutions will be studied. The continuous dependence of the unique solution in x ∈ L₁[0, T] will be studied. We study the uniqueness of the solution x ∈ C [0,1], and the continuous dependence of the unique solution will be studied. We study x ∈ C [0,1]. We additionally provide examples given as the same application of the result.

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Published

2026-10-03

How to Cite

Somyya Amrajaa, Imparak Sulayman, Abdulbari Jawwad. Stability and Continuous Dependence of the Solution of a Set-Valued Functional Equation with the Parameter. Alq J Med App Sci [Internet]. 2026 Oct. 3 [cited 2026 Oct. 3];:3168-72. Available from: https://journal.utripoli.edu.ly/index.php/Alqalam/article/view/1980