Analysis reveals fixed point theorem based on metrics of sigma-noncompactness in topological spaces, suggesting potential implications for functional analysis.
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.
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Caponetti et al. (2025) studied this question.
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