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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Articles in the same Issue
- A new categorical equivalence for stone algebras
- On special classes of prime filters in BL-algebras
- A note on characterized and statistically characterized subgroups of 𝕋 = ℝ/ℤ
- New Young-type integral inequalities using composition schemes
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- Jensen-type inequalities for a second-order differential inequality condition
- A direct proof of the characterization of the convexity of the discrete Choquet integral
- Envelope of plurifinely plurisubharmonic functions and complex Monge-Ampère type equation
- Fekete-Szegö inequalities for Φ-parametric and β-spirllike mappings of complex order in ℂn
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