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

Lower strict monotonicity points and lower local uniform monotonicity points are considered in the case of Musielak-Orlicz function spaces L-Phi 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.