DOI: 10.24193/fpt-ro.2025.2.15

Authors: Noura Laksaci, Ahmed Boudaoui and Bilel Krichen

Abstract: This paper is concerned with some fixed point theorems in generalized Banach algebras. Our fundamental results are detailed regarding in terms of the lack of compactness by using set-contractive operators with respect to some generalized measures of noncompactness. The obtained results are further applied to a certain coupled system for impulsive differential equations defined in the generalized Banach algebra 𝒫𝒞([0,1], ℝ) × 𝒫𝒞([0,1], ℝ) of all couple of piecewise continuous functions on [0,1].

Key Words and Phrases: Generalized Banach algebra, fixed point theorems, M-set contractive, generalized measure of noncompactness, system for impulsive differential equations.

2010 Mathematics Subject Classification: 47H10, 54H25, 47H08.

Published on-line: May 1st, 2025.

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