2021/04/28 by Debmalya Sain, Sain, Debmalya, Saikat Roy +1 · 1 citation
Decision Sciences · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Approximation and Integration #Multi-Criteria Decision Making #Primary 46B28 #Secondary 46B20
paper · pdf · doi:10.48550/arxiv.2104.14003
openalex publication_date 2021/04/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance formulae are presented. As an application of our study, we obtain some crucial inequalities, which also strengthen the classical Hölder's inequality. The relevance of the algorithms and the inequalities are discussed through concrete examples.