Abstract
Given an F-space (X, τ) and σ ≤ τ a linear topology on X, this paper provides the definition of a general set function that allows us to define measures of σ-noncompactness in X. In particular, we construct measures of nonconvex σ-noncompactness that are monotonic, invariant under passage to the closed convex hull, and satisfy the Cantor intersection property. Additionally, we derive a fixed point theorem for maps that satisfy the classical Darbo condition with respect to a given measure of nonconvex σ-noncompactness.
Funding statement: This research has been accomplished within the UMI Group TAA Approximation Theory and Applications, the GNAMPA of INdAM. The first author has been supported by FFR-2024, University of Palermo.
Acknowledgement
The authors would like to thank the anonymous referee for carefully reading the manuscript and providing useful comments that improved the presentation of this paper.
(Communicated by David Buhagiar)
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