New Functional Inequalities with Applications to the Arctan-Fast Diffusion Equation
Sign Up to like & getrecommendations! Published in 2024 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-025-02842-1
Abstract: In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads ∫S1arctan∂xuu∂xudx⩾arctanuW˙1,1(S1)uW˙1,1(S1).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}… read more here.
Keywords: arctan fast; diffusion equation; document; fast diffusion ... See more keywords
Monotonicity and functional inequalities for the complete p-elliptic integrals
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.04.025
Abstract: Abstract Takeuchi's generalized complete elliptic integrals related to generalized trigonometric functions are of importance in the computation of the generalized pi and in the elementary proof of Ramanujan's cubic transformation. In this paper we generalize… read more here.
Keywords: inequalities complete; elliptic integrals; monotonicity functional; functional inequalities ... See more keywords
Functional inequalities for the Wright functions
Sign Up to like & getrecommendations! Published in 2017 at "Integral Transforms and Special Functions"
DOI: 10.1080/10652469.2016.1254628
Abstract: ABSTRACT In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarević-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for… read more here.
Keywords: inequalities wright; wright functions; functions functional; functional inequalities ... See more keywords
Functional inequalities related to Sobolev, Besov and Morrey spaces in the Dunkl setting
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DOI: 10.1515/forum-2024-0481
Abstract: Abstract In this paper we investigate the Sobolev inequality in the Dunkl setting using the semigroup theory and a nonlocal calculus for the fractional Dunkl operator. As an application and improvement, we further study some… read more here.
Keywords: related sobolev; morrey spaces; inequalities related; sobolev besov ... See more keywords
Additive s-functional inequalities and partial multipliers in Banach algebras
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Inequalities"
DOI: 10.7153/jmi-2019-13-60
Abstract: In this paper, we solve the additive s -functional inequalities ‖ f (x+ y− z)− f (x)− f (y)+ f (z)‖ ‖s( f (x− y)+ f (y− z)− f (x− z))‖, (0.1) where s is… read more here.
Keywords: banach algebras; functional inequalities; partial multipliers; inequalities partial ... See more keywords