Non-squareness properties of Orlicz spaces equipped with the -Amemiya norm

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

“…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]. …”

“…By the p-Amemiya norm of a function x ∈ L 0 (μ) we mean the number x Φ,p defined by the formula (see [5,6,7])…”

“…For more informations about Orlicz spaces, we refer to [2,17,21] and for Orlicz spaces equipped with p-Amemiya norm to [5,6,7]. …”

Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $$\mathbb {R}^{2}$$ R 2

“…for any (u, ν) ∈ R 2 , was considered in the papers [10,11,14,15], the fixed point property in these spaces was studied in [14,20]. The dominated best approximation in these spaces was studied in [14].…”

“…where 1 ≤ p ≤ ∞ (see [10,11,14,15,20]). The norm • Φ,1 is the Orlicz norm • 0 Φ which was defined by Orlicz in [39] by the formula…”