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

Abstract

In this paper, the necessary and sufficient conditions for the upper strict monotonicity point and the upper local uniform monotonicity point are given in the case of Musielak–Orlicz spaces equipped with the Mazur–Orlicz F-norm. Moreover, strict monotonicity and upper local uniform monotonicity are easily deduced in the case of Musielak–Orlicz spaces endowed with the Mazur–Orlicz F-norm, and the work by Kaczmarek presented in the references is encompassed by the corollaries presented in this paper.