arXiv subjects

Doan Huu Hieu

Publications and source records attributed to Doan Huu Hieu.

3 recordsLinked to original sources

arXiv2026

Norm Minimisation Problems Involving Distances to Convex Sets

The paper studies product-space norm minimisation problems involving distances to convex sets. Using standard tools from convex and functional analysis, we establish complete dual necessary and sufficient optimality conditions and show that the entire solution set can be constructed from the dual vectors arising from the optimality conditions at a given solution. As a consequence, we study optimality conditions and solution set descriptions for generalised versions of the Fermat-Torricelli problem, the Chebyshev centre problem, and the p-Fermat-Torricelli problem. Comparisons with existing results are provided whenever applicable. Examples in finite and infinite dimensional spaces equipped with different norms are presented to illustrate the results.

math.OC↗

arXiv2026

A von Neumann-Jordan Constant of Non-Normable Metrics

The paper studies a generalized von Neumann-Jordan constant of non-normable metrics on vector spaces. To the best of our knowledge, all existing results of the von Neumann-Jordan constant and its generalizations have been established only in the normed setting. We identify reasonable conditions on non-normable metrics under which results known for norms remain valid. Several examples and counterexamples are provided to justify the established results. The computation for a class of non-normable metrics on product spaces is also investigated. In particular, we give precise formulas for the generalized von Neumann-Jordan constant of p-metrics under a metric-type Clarkson inequality. Comparisons with existing results are discussed throughout the paper whenever applicable.

math.FA↗

arXiv2026

Metric constructions and fixed point theorems in product spaces

The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are topologically equivalent to the conventional ones. As an application, we study fixed point and approximate fixed point properties for nonexpansive maps on a product space equipped with the constructed metric. We show that existing fixed point results of this type are consequences of our framework. Examples are provided to illustrate the established results. The construction machinery is also used to study products of length and geodesic spaces. The obtained results encompass existing ones and provide a background for potential studies of fixed point properties on these product spaces.

math.MG↗