On three duality results
M. D. Voisei, C. Zalinescu
TL;DR
This paper provides counterexamples to two duality theorems in the literature and refines a related duality result, contributing to the theoretical understanding of duality in mathematical analysis.
Contribution
It introduces specific counterexamples to existing duality results and improves a related theorem, advancing the theoretical framework of duality principles.
Findings
Counterexamples disprove two existing duality results
A refined version of a duality theorem is presented
The results clarify limitations and conditions of duality theorems
Abstract
The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].
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Taxonomy
TopicsFixed Point Theorems Analysis · Optimization and Variational Analysis · Holomorphic and Operator Theory