Fixed-Point Theorem with a Novel Contraction Approach in Banach Algebras

Hamza El Bazi (), Younes Lahraoui, Cheng-Chi Lee (), Loubna Omri and Abdellatif Sadrati
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Hamza El Bazi: LMPA Laboratory, MASD Group, Department of Mathematics, FST Errachidia, University Moulay Ismaïl of Meknes, B.P. 509, Errachidia 52000, Morocco
Younes Lahraoui: Mathematics, Computer Science and Applications TEAM, Abdelmalek Essaâdi University, ENSA, Tangier 90000, Morocco
Cheng-Chi Lee: Department of Library and Information Science, Fu Jen Catholic University, New Taipei City 24205, Taiwan
Loubna Omri: FSJES of Tetouan, Abdelmalek Essaâdi University, Tetouan 93030, Morocco
Abdellatif Sadrati: LMPA Laboratory, MASD Group, Department of Mathematics, FST Errachidia, University Moulay Ismaïl of Meknes, B.P. 509, Errachidia 52000, Morocco

Mathematics, 2025, vol. 13, issue 18, 1-9

Abstract: In this paper, we establish a fixed-point theorem for mixed monotone operators in ordered Banach algebras by introducing a novel contraction condition formulated in terms of the product law, which represents a significant departure from the traditional additive approach. By exploiting the underlying algebraic structure, our method ensures both the existence and uniqueness of fixed points under broader conditions. To illustrate the effectiveness of the proposed theorem, we also provide a concrete example that demonstrates its applicability.

Keywords: ordered Banach algebra; mixed monotone operators; coupled lower and upper fixed point; fixed point in Banach algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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