We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

Let D be the open unit disk in the complex plane C, H(D) the class of all analytic functions on D and φ an analytic self-map of D. In order to unify the products of composition, multiplication, and differentiation operators, Stević and Sharma introduced the following so-called Stević-Sharma operator on H(D): Tψ1,ψ2,φf(z) = ψ1(z)f(φ(z)) + ψ2(z)f ′(φ(z)), where ψ1, ψ2 ∈ H(D). By constructing some...

Abstract The necessary and sufficient conditions for both the Kadec–Klee property as well with respect to coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped Orlicz norm generated by arbitrary functions any non-increasing weight sequences are given. Moreover, their subspaces of elements an order continuous full characterization is presented. Some tools useful proofs main resul...

We introduce the class of (k,h) -convex functions defined on k -convex domains, and we prove some new inequalities of Hermite-Hadamard and Fejér type for such mappings. This generalizes results given for h -convex functions in [1, 17], and for s -Orlicz convex mappings in [4]. Mathematics subject classification (2010): Primary: 26A51, 26D15; Secondary: 52A30.

We present a proof that in Orlicz spaces the Amemiya norm and the Orlicz norm coincide for any Orlicz function ‘p. This gives the answer for an open problem. We also give a description of the Amemiya type for the Mazur-Orlicz F-norm.

Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty lo, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz–Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a...