Lower Local Uniform Monotonicity in F-Normed Musielak–Orlicz Spaces

Abstract

Lower strict monotonicity points and lower local uniform monotonicity points are considered in the case of Musielak–Orlicz function spaces LΦ endowed with the Mazur–Orlicz F-norm. The findings outlined in this study extend the scope of geometric characteristics observed in F-normed Orlicz spaces, as well as monotonicity properties within specific F-normed lattices. They are suitable for the Orlicz spaces of ordered continuous elements, specifically in relation to the Mazur–Orlicz F-norm. In addition, in this paper presents results that can be used to derive certain monotonicity properties in F-normed Musielak–Orlicz spaces.

Keywords

• Musielak–Orlicz spaces
• Mazur–Orlicz F-norm
• F-norm K<i>ö</i>the spaces
• lower strict monotonicity point
• lower local uniform monotonicity point