Global Existence and Uniqueness of Solutions of Integral Equations with Multiple Variable Delays and Integro Differential Equations: Progressive Contractions

Osman Tunç (), Cemil Tunç and Jen-Chih Yao
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Osman Tunç: Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404, Taiwan

Mathematics, 2024, vol. 12, issue 2, 1-16

Abstract: In this work, we delve into a nonlinear integral equation (IEq) with multiple variable time delays and a nonlinear integro-differential equation (IDEq) without delay. Global existence and uniqueness (GEU) of solutions of that IEq with multiple variable time delays and IDEq are investigated by the fixed point method using progressive contractions, which are due to T.A. Burton. We prove four new theorems including sufficient conditions with regard to GEU of solutions of the equations. The results generalize and improve some related published results of the relevant literature.

Keywords: GEU of solutions; integral equation; integro-differential equation; variable time delay; fixed point; progressive contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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