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

Author

Listed:
  • 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
    Department of Computer Science and Information Engineering, Fintech and Blockchain Research Center, Asia University, Taichung 41354, 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)

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.

Suggested Citation

  • Hamza El Bazi & Younes Lahraoui & Cheng-Chi Lee & Loubna Omri & Abdellatif Sadrati, 2025. "Fixed-Point Theorem with a Novel Contraction Approach in Banach Algebras," Mathematics, MDPI, vol. 13(18), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:3024-:d:1752966
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