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March 17, 2026TURKISH JOURNAL OF MATHEMATICS0 citationsOpen Access

The degree of nondensifiability in Hausdorff locally convex topological vector spaces and applications

Key Points

This paper aims to explore the degree of nondensifiability in Hausdorff locally convex topological vector spaces (LCTVS) and its applications.
Defined the degree of nondensifiability (DND) for Hausdorff LCTVS.
Compared DND properties in Hausdorff LCTVS with those in Banach spaces.
Investigated fixed point results under specific conditions.
Established key properties of DND in LCTVS.
Demonstrated fixed point results applicable to LCTVS.
Proved existence of solutions for certain Volterra integral equations.

Abstract

The so called degree of nondensifiability, DND, has been studied in Banach spaces through several studies, and some fixed point results using the DND have been proved. In the present paper, we extend the concept of DND to a Hausdorff locally convex topological vector space (LCTVS). Its main properties, as well as the differences between the DND in Banach spaces and the DND in a LCTVS, are analyzed. Furthermore, under suitable conditions, we provide some fixed point results in a LCTVS by using the DND, and as an application, we prove the existence of solutions of certain Volterra integral equations.

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