Results 71 to 80 of about 8,406 (194)

The De Giorgi method for local and nonlocal systems

Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.
Abstract We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems.
Linus Behn, Lars Diening, Simon Nowak, Toni Scharle   +3 more
wiley   +1 more source

Convex functions on dual Orlicz spaces [PDF]

Positivity, 2019
In the dual $L_{ ^*}$ of a $ _2$-Orlicz space $L_ $, that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology $ (L_{ ^*},L_ )$ if and only if on each order interval $[- , ]=\{ : - \leq \leq \}$ ($ \in L_{ ^*}$), it is lower semicontinuous ...
Freddy Delbaen, Keita Owari
openaire   +2 more sources

Global second‐order estimates in anisotropic elliptic problems

Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.
Abstract This work deals with boundary value problems for second‐order nonlinear elliptic equations in divergence form, which emerge as Euler–Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of the gradient of trial functions.
Carlo Alberto Antonini, Andrea Cianchi, Giulio Ciraolo, Alberto Farina, Vladimir Maz'ya   +4 more
wiley   +1 more source

Locally Nearly Uniformly Convex Points in Orlicz Spaces Equipped with the Luxemburg Norm

Axioms
This research explores two novel geometric concepts—nearly convex points and locally nearly uniformly convex points within the frameworks of Banach spaces and Orlicz spaces equipped with the Luxemburg norm.
Yunan Cui, Xiaoxia Wang, Yaoming Niu
doaj   +1 more source

Equivalent theorem of approximation by linear combination of weighted Baskakov–Kantorovich operators in Orlicz spaces

Journal of Inequalities and Applications, 2019
In this paper, we introduce the Orlicz space corresponding to the Young function and, by virtue of the equivalent theorem between the modified K-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for linear ...
Ling-Xiong Han, Bai-Ni Guo, Feng Qi
doaj   +1 more source

On multiparametrized integral inequalities via generalized α‐convexity on fractal set

Mathematical Methods in the Applied Sciences, Volume 48, Issue 1, Page 980-1002, 15 January 2025.
This article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized α$$ \alpha $$‐convex functions. It introduces a novel extension of the Hermite‐Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity.
Hongyan Xu, Abdelghani Lakhdari, Fahd Jarad, Thabet Abdeljawad, Badreddine Meftah   +4 more
wiley   +1 more source

On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces

Mathematics, 2018
In this paper, the authors introduce the Orlicz spaces corresponding to the Young function and, by virtue of the equivalent theorem between the modified K-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for ...
Ling-Xiong Han, Feng Qi
doaj   +1 more source

An Innovative Approach to the Product of k‐Hybrid Functional Integral Equation

Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.
In this paper, our study focuses on exploring the solutions of a product of k‐hybrid functional integral equation which is characterized by multiple delays. We prove the existence of continuous, well‐defined, and bounded solutions on the semi‐infinite interval.
A. M. A. El-Sayed, Sh. M. Al-Issa, Deepali   +2 more
wiley   +1 more source

A Characterization of Riesz Potential and Its Commutator in Local Complementary Generalized Orlicz–Morrey Spaces

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this paper, we find sufficient conditions on functions ω1, ω2 which ensure the boundedness of Riesz potentials and their commutators with BMO functions from one local complementary generalized Orlicz–Morrey spaces M ∁Φ,ω1x0ℝn to the spaces M ∁Ψ,ω2x0ℝn. As a consequence of the boundedness of the Riesz potential, we give the boundedness the fractional
Canay Aykol, Javanshir J. Hasanov, Ayhan Serbetci, Andrea Scapellato   +3 more
wiley   +1 more source

ON \(\lambda\)-WEAK CONVERGENCE OF SEQUENCES DEFINED BY AN ORLICZ FUNCTION

Ural Mathematical Journal
In this article, we introduce and rigorously analyze the concept of difference \(\lambda\)-weak convergence for sequences defined by an Orlicz function.
Ömer Kişi, Mehmet Gürdal
doaj   +1 more source