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

摘要

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 L-Phi,L-p are given in the most general case of Orlicz function Phi. and for all 1 <= p <= infinity. Finally, some applications of the results to the best dominated approximation problems are presented. This paper is a continuation of the studies from [5-7]. (C) 2015 Elsevier Inc. All rights reserved.