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Existence Results for a Coupled System of Perturbed Functional Differential Inclusions in Banach Algebras

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Abstract

In this paper, we establish some new fixed point theorems for a \(2\times 2\) block operator matrix defined on nonempty, bounded, closed, and convex subsets of Banach algebras, where the inputs are multi-valued mappings. The obtained results are then applied to a coupled system of perturbed functional differential inclusions of initial and boundary value problems in order to prove the existence of solutions under a Carathéodory condition.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Soukra Road Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

    Aref Jeribi

  2. Département de Mathématiques et Informatique, Faculté des Sciences Techniques de Sidi Bouzid, Campus universitaire cité agricole, Sidi Bouzid, Tunisia

    Najib Kaddachi

  3. Department of Mathematics, Preparatory Engineering Institute, University of Sfax, Menzel Chaker Road Km 0.5, B.P. 1172, 3018, Sfax, Tunisia

    Bilel Krichen

Authors
  1. Aref Jeribi
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  2. Najib Kaddachi
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  3. Bilel Krichen
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Correspondence to Bilel Krichen.

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Communicated by See Keong Lee.

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Jeribi, A., Kaddachi, N. & Krichen, B. Existence Results for a Coupled System of Perturbed Functional Differential Inclusions in Banach Algebras. Bull. Malays. Math. Sci. Soc. 41, 893–918 (2018). https://doi.org/10.1007/s40840-016-0374-7

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  • DOI: https://doi.org/10.1007/s40840-016-0374-7

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