ON LOCAL CONVEXITIES OF ORLICZ SPACES ENDOWED WITH s-NORMS

Basar E., Oztop S.

COLLOQUIUM MATHEMATICUM, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.4064/cm9702-10-2025
  • Journal Name: COLLOQUIUM MATHEMATICUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Istanbul University Affiliated: Yes

Abstract

Let Phi be an Orlicz function and L Phi (X, Sigma, & micro;) be the corresponding Orlicz space on a non-atomic, sigma-finite, complete measure space (X, Sigma, & micro;). We describe the local uniform convexity of Orlicz spaces endowed with the s-norm and discuss the weak and compact variants of this property. Also, we derive some results in approximation theory, concerning best approximations and farthest points. Thus, our study provides a comprehensive generalization of several results that have been obtained for Orlicz spaces with the Orlicz norm and the Luxemburg norm.