Results 111 to 120 of about 22,314 (145)
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Commentationes Mathematicae Universitatis Carolinae, 2021
Summary: We investigate which points in the unit sphere of the Besicovitch-Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.
Hassaine, Slimane, Boulahia, Fatiha
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Summary: We investigate which points in the unit sphere of the Besicovitch-Orlicz space of almost periodic functions, equipped with the Luxemburg norm, are extreme points. Sufficient conditions for the strict convexity of this space are also given.
Hassaine, Slimane, Boulahia, Fatiha
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On Some Convexity Properties of Orlicz Sequence Spaces Equipped with the Luxemburg Norm
Mathematische Nachrichten, 1997AbstractRotundity of finite ‐dimensional Orlicz spaces lϕn equipped with the Luxemburg norm is considered. It is proved that criteria for rotundity of lϕnfor n ≥ 3 does not depend on n and are the same as the criteria for rotundity of the inhite‐dimensional subspace hϕ of an Orlicz sequence spacelϕ. Criteria for rotundity of lϕ2 are different.
Hudzik, H., Pallaschke, Diethard
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Points of monotonicity in Musielak-Orlicz function spaces endowed with the Luxemburg norm
Archiv der Mathematik, 2004For a Banach function lattice \(X\) with the cone \(X^+\) of its positive elements, let \(S(X^+)= S(X)\cap X^+\), \(S(X)\) being the unit sphere in \(X\). Let \(L_M\) be a Musielak-Orlicz space with Luxemburg norm and \(E_M\) the subspace of finite elements of \(L_M\).
Hudzik, H., Liu, X. B., Wang, T. F.
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Erratum to the paper “Smooth Points of Orlicz Spaces Equipped with Luxemburg Norm”
Mathematische Nachrichten, 1994Minor corrections to the paper cited in the title [ibid. 155, 31-45 (1992; Zbl 0795.46016)].
Grząślewicz, R., Hudzik, H.
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On Some Local Geometry of Orlicz Sequence Spaces Equipped with the Luxemburg Norm
Acta Mathematica Hungarica, 1998Criteria for strong \(U\)-points, compactly locally uniformly rotund points, weakly compactly locally uniformly rotund-points and locally uniformly rotund-points in Orlicz sequence spaces equipped with the Luxemburg norm are given and several relations among them are found. It is also shown that in any Banach space \(X\) strong \(U\)-points are exposed
Cui, Y., Hudzik, H., Meng, C.
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K-extreme point of generalized orlicz sequence spaces with Luxemburg norm
Commentationes Mathematicae, 2013In this paper,we give necessary and sufficient conditions in order that a point \(u\in S(l_{({\it \Phi})})\) is a k-extreme point in generalized Orlicz sequence spaces equipped with the Luxemburg norm, combing the methods used in classical Orlicz spaces and new methods introduced especially for generalized ones.
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Nonlinear Analysis: Theory, Methods & Applications, 1999
Consider \(\varphi =(\varphi _{i})_{i=1}^{\infty }\) a Musielak-Orlicz function (i.e. \(\varphi _{i}\) is a Orlicz function for every \(i\)) and \(\ell ^{\varphi }=\{x\in \ell ^{0}\mid \sum_{i=1}^{\infty }\varphi _{i}(\lambda x_{i})0\}\) the Musielak-Orlicz sequence space.
Cui, Yunan, Hudzik, Henryk
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Consider \(\varphi =(\varphi _{i})_{i=1}^{\infty }\) a Musielak-Orlicz function (i.e. \(\varphi _{i}\) is a Orlicz function for every \(i\)) and \(\ell ^{\varphi }=\{x\in \ell ^{0}\mid \sum_{i=1}^{\infty }\varphi _{i}(\lambda x_{i})0\}\) the Musielak-Orlicz sequence space.
Cui, Yunan, Hudzik, Henryk
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k-I-uniform convexity of Orlicz-Lorentz spaces endowed with the Luxemburg norm
Journal of Mathematical Analysis and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zichen Wang, Wanzhong Gong
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Smooth Points of O
AbstractSmooth points of the unit sphere of ORLICZ spaces equipped with LUXEMBURG norm are characterized for a non‐atomic measure as well as for the counting measure. As a corollary, a criterion of smoothness of ORLICZ spaces with LUXEMBURG norm is obtained.
Grzaślewicz, R., Hudzik, H.
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Proceedings of the American Mathematical Society, 2013
Summary: The asymptotic behavior of a sequence of functionals involving the Luxemburg norm of the gradient in variable exponent Lebesgue spaces is studied in the framework of \(\Gamma\)-convergence. As a consequence, we prove the convergence of minima for closely related functionals to a corresponding quantity associated to the \(\Gamma\)-limit.
Bocea, Marian, Mihăilescu, Mihai
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Summary: The asymptotic behavior of a sequence of functionals involving the Luxemburg norm of the gradient in variable exponent Lebesgue spaces is studied in the framework of \(\Gamma\)-convergence. As a consequence, we prove the convergence of minima for closely related functionals to a corresponding quantity associated to the \(\Gamma\)-limit.
Bocea, Marian, Mihăilescu, Mihai
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