Some generalizations of Darbo's fixed point theorem under weak topology features with application to a Volterra-type integral equation
Submitted: 2023-10-14
|Accepted: 2025-01-29
|Published: 2025-04-01
Copyright (c) 2025 Mohamed Khazou, Abdelmjid Khchine
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
weak-topology, measure of weak noncompactness, Volterra-type integral equations, fixed point theorem, coupled fixed point, weakly sequentially continuous operator, ws-compact operator
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Abstract:
In this paper, we provide some generalizations of Darbo's fixed point theorem for larger classes of contraction. Our results are investigated under the weak topology of a Banach space using the measure of weak noncompactness. The results presented in the paper generalize and extend several well-known comparable results in the literature. Further, We illustrate the applicability of our theoretical findings by studying the existence of solutions for a coupled of nonlinear Volterra-type integral equations.
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