On measures of σ-noncompactess in F-spaces

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.