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Uniform rotundity of Orlicz function spaces equipped with the p ‐Amemiya norm
Author(s) -
Kaczmarek Radosław
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700025
Subject(s) - mathematics , norm (philosophy) , mathematical analysis , pure mathematics , law , political science
Necessary and sufficient conditions for uniform rotundity of Orlicz function spaces equipped with the p‐Amemiya norm ( 1 ≤ p ≤ ∞ ) are presented. The obtained results unify, complete and widen the characterization of uniform rotundity of Orlicz spaces. In the case of the ∞‐Amemiya (i.e. the Luxemburg) norm or the 1‐Amemiya (i.e. the Orlicz) norm, these results were known earlier. Some connections with the fixed point theory and the best approximation theory are presented.