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

Ahmed Boudaoui (), Bilel Krichen (), Noura Laksaci () and Donal O’Regan ()
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Ahmed Boudaoui: University of Adrar
Bilel Krichen: University of Sfax
Noura Laksaci: University of Adrar
Donal O’Regan: National University of Ireland

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 532-546

Abstract: 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 $$\mathcal {{ C }} (J , E_{1} )\times \mathcal {{ C }} (J , E_{2} ) $$ C ( J , E 1 ) × C ( J , E 2 ) of all continuous functions on $$J = [ 0 , { T } ] $$ J = [ 0 , T ] to illustrate our theory.

Keywords: Generalized Banach space; Fixed point theorems; M-contraction; Generalized Dunford-Pettis spaces; Integral equations system; 47H10; 54H25; 45G15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00273-2

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