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1

On perturbed quadratic integral equations and initial value problem with nonlocal conditions in Orlicz spaces

Metwali Mohamed M. A.

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

86--94

EN

The existence of a.e. monotonic solutions for functional quadratic Hammerstein integral equations with the perturbation term is discussed in Orlicz spaces. We utilize the strategy of measure of noncompactness related to the Darbo fixed point principle. As an application, we discuss the presence of solution of the initial value problem with nonlocal conditions.

2

Henryk Hudzik : vita et opera

Mastyło M., Musielak J.

Commentationes Mathematicae

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2015

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Vol 55, No. 2

45--78

EN

This article contains a short vita of Henryk Hudzik's as well as a non-exhaustive survey of his contribution to various areas of analysis. We focus on the theory of Orlicz−Sobolev spaces and the geometry of Banach spaces. We highlight criteria for some important geometric properties related to the metric fixed point theory in some classes of Banach lattices, including Orlicz and Orlicz−Lorentz spaces, but we do not forget Henryk Hudzik's contribution to nonlinear integral equations and partial differential equations.

3

Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

Costarelli D., Vinti G.

Commentationes Mathematicae

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2013

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Vol. 53, No. 2

171--192

EN

In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence in Lp-spaces, 1 ≤ p < ∞, very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fejér and B-spline kernels are also considered.

4

Asymptotically isometric and isometric copies of ℓ1 in some Banach function lattices

Kamińska A., Mastyło M.

Commentationes Mathematicae

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2013

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Vol. 53, No. 2

283--300

EN

We identify the class of Calderón-Lozanovskii spaces that do not contain an asymptotically isometric copy of ℓ1, and consequently we obtain the corresponding characterizations in the classes of Orlicz-Lorentz and Orlicz spaces equipped with the Luxemburg norm. We also give a complete description of order continuous Orlicz-Lorentz spaces which contain (order) isometric copies of ℓ1(n) for each integer n≥2. As an application we provide necessary and sufficient conditions for order continuous Orlicz-Lorentz spaces to contain an (order) isometric copy of ℓ1. In particular we give criteria in Orlicz and Lorentz spaces for (order) isometric containment of ℓ1(n) and ℓ1. The results are applied to obtain the description of universal Orlicz-Lorentz spaces for all two-dimensional normed spaces.

5

Best Constants for the Inequalities between Equivalent Norms in Orlicz Spaces

Bang H. H., Hoang N. V., Huy V. N.

Bulletin of the Polish Academy of Sciences. Mathematics

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2011

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Vol. 59, no 2

165--174

EN

We investigate best constants for inequalities between the Orlicz norm and Luxemburg norm in Orlicz spaces.

6

J-convexity constants

Wang J.

Opuscula Mathematica

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2007

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Vol. 27, no. 1

167-174

EN

We introduce the J-convexity constants on Banach spaces and give some properties of the constants. We give the relations between the J-convexity constants and the n-th von Neumann-Jordan constants. Using the quantitative indices we estimate the value of J-convexity constants in Orlicz spaces.

7

Generalized mixed topology on F-normed function spaces

Kasior E., Nowak M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2004

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Vol. 44, nr 1

55--66

EN

Let (X, ||•||) be a F-normed function space over a σ-finite measure space (Ω, Σ, μ) and let ||•||0 denote the usual F-norm on L0 that generates the convergence in measure on subsets of finite measures. In X a natural two-normed convergence can be defined as follows: a sequence (xn) in X is said to be γ-convergent to x ϵ X whenever || xn - x||0 → 0 and supn||xn|| < ∞. In this paper we study locally solid topologies on X satisfying the continuity property with respect to this γ-convergence in X. We call such topologies "uniformly Lebesgue". These investigations are closely related to the theory of generalized inductive limit topologies in the sense of Turpin. In particular we show that a generalized mixed topology γT(Tφ, T0|Lφ) on the Orlicz space Lφ (φ is not assumed to be convex) is the finest uniformly Lebesgue topology on Lφ. Moreover, we characterize γφ-linear functionals on Lφ.

8

An inequality of Bohr and Favard for Orlicz spaces

Bang H.

Bulletin of the Polish Academy of Sciences. Mathematics

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2001

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Vol. 49, no 4

381-387

EN

In this paper, we prove an inequality of Bohr and Favard for any Orlicz norm (with the same constants as in the Bohr-Favard inequality).

9

Weak-sequential compactness on non-locally convex Orlicz spaces

Nowak M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 3

225-231

EN

Let [L^fi] be an Orlicz space defined by a finite valued Orlicz function [fi] (not necesarilly convex) over a [sigma]-finite atomless measure space. Let (L^fi[...] be the order continous dual of [L^fi]. It is proved that a subset Z of [L^fi] is conditionally sequentially sigma([L^fi],(L^fi])[...)-compact (i.e., every sequence in Z contains a sigma([L^[fi],(L^fi])[...])-Cauchy subsequence) if and only if Z is norm bounded in some Orlicz space [L^psi] where psi increases more rapidly than [...] (the convex minorant of fi).