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Fixed point theorems in generalized Banach spaces under G-weak topology features

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Abstract

In this paper we extend some fixed point results in generalized Banach spaces endowed with the so-called G-weak topology and having the generalized Dunford–Pettis property (in short, G-DP property). Our main results are formulated in terms of G-weak compactness and G-weak sequential continuity. Also we give an example for a coupled system of nonlinear integral equations defined on the generalized Banach space \(\mathcal {{ C }} (J , E_{1} )\times \mathcal {{ C }} (J , E_{2} ) \) of all continuous functions on \(J = [ 0 , { T } ] \) to illustrate our theory.

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Authors and Affiliations

  1. Laboratory of Mathematics Modeling and Applications, University of Adrar, Adrar, Algeria

    Ahmed Boudaoui & Noura Laksaci

  2. Department of Mathematics and Computer science, University of Adrar, National Road No. 06, 01000, Adrar, Algeria

    Ahmed Boudaoui & Noura Laksaci

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

    Bilel Krichen

  4. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Ahmed Boudaoui
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  2. Bilel Krichen
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  3. Noura Laksaci
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  4. Donal O’Regan
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Correspondence to Ahmed Boudaoui.

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Communicated by Rahul Roy.

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Boudaoui, A., Krichen, B., Laksaci, N. et al. Fixed point theorems in generalized Banach spaces under G-weak topology features. Indian J Pure Appl Math 54, 532–546 (2023). https://doi.org/10.1007/s13226-022-00273-2

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  • DOI: https://doi.org/10.1007/s13226-022-00273-2

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