Monotonicity properties and dominated best approximation problems in Orlicz spaces equipped with the p-Amemiya norm

In this paper strict monotonicity, lower and upper uniform monotonicities, uniform monotonicity as well as decreasing and increasing uniform monotonicities of Orlicz spaces equipped with the p  -Amemiya norm are studied. Criteria for these six properties in the Orlicz spaces LΦ,pLΦ,p are given in the most general case of Orlicz function Φ and for all 1≤p≤∞1≤p≤∞. Finally, some applications of the results to the best dominated approximation problems are presented. This paper is a continuation of the studies from [5], [6] and [7].