Rotundity and uniform rotundity of Orlicz‐Lorentz sequence spaces equipped with the Orlicz norm

Abstract

In this paper, we shall give a criteria of the rotundity and uniform rotundity of Orlicz-Lorentz sequence spaces equipped with the Orlicz norm.

Non-squareness and local uniform non-squareness properties of Orlicz-Lorentz function spaces endowed with the Orlicz norm

“…In 2012, Wang and Chen extended the definition and properties of [24] to γ ≤ ∞ [23] , and get the following two lemmas.…”

I‐convexity and Q‐convexity in Orlicz–Bochner function spaces endowed with the Orlicz norm

“…Lemma () (1) If and , then for any , there exist and such that holds for all satisfying and . If and , then for every and , there exist and such that …”

Kadec–Klee properties of Orlicz–Lorentz sequence spaces equipped with the Orlicz norm

“…x * (i)y * (i)ω(i) : I ,ω (y) ≤ 1 appeared (see [15,33] and also [7]). In [8] it was shown that for arbitrary Orlicz function and any non-increasing weight function ω, equality…”

“…Recall that Orlicz-Lorentz spaces, which are a natural generalization of Orlicz and Lorentz spaces, were introduced in the early nineties of the twentieth century [18,24,27]. These investigations gave an impulse to further study of the spaces, results of which have been published among others in papers [1,3,7,[10][11][12][13][14][15]19,22,33].…”