Results 1 to 10 of about 25,201 (167)

A family of functional inequalities: Łojasiewicz inequalities and displacement convex functions

Journal of Functional Analysis, 2018
For displacement convex functionals in the probability space equip\-ped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Łoja\-sie\-wicz inequalities. \chg{We also discuss the more general case of $λ$-convex functions and we provide a general convergence theorem for the corresponding gradient dynamics.
Jérôme Bolte, , Adrien Blanchet
exaly   +8 more sources

ON FUNCTIONAL INEQUALITIES FOR THE PSI FUNCTION

Проблемы анализа
Motivated by the works of Bougotta and Mercer, the authors in this paper study the monotonicity of the function x↦ψ(1+bx)^a/ψ(1+ax)^b, and establish several inequalities involving the psi function.
Barkat A. Bhayo, Liyao Xie, Sebnem Yildiz Yar   +2 more
doaj   +3 more sources

Integral Inequalities Involving Strictly Monotone Functions

Mathematics, 2023
Functional inequalities involving special functions are very useful in mathematical analysis, and several interesting results have been obtained in this topic.
Mohamed Jleli, Bessem Samet
doaj   +1 more source

Functional inequalities for the Bickley function [PDF]

Mathematical Inequalities & Applications, 2014
In this paper our aim is to deduce some complete monotonicity properties and functional inequalities for the Bickley function. The key tools in our proofs are the classical integral inequalities, like Chebyshev, Hölder-Rogers, Cauchy-Schwarz, Carlson and Grüss inequalities, as well as the monotone form of l'Hospital's rule.
Baricz, Árpád, Pogány, Tibor K.
openaire   +4 more sources

Inequalities for the Beta function [PDF]

Mathematical Inequalities & Applications, 2015
Let g(x):= (e/x)xΓ(x+1) and F(x,y):= g(x)g(y)/g(x+y). Let Dx,y (k) be the k th differential in Taylor's expansion of logF(x,y) . We prove that when (x,y) ∈ R+ 2 one has (-1)k-1Dx,y (k) (X,Y) > 0 for every X,Y ∈ R+, and that when k is even the conclusion holds for every X,Y ∈ R with (X,Y) = (0,0).
Grenié, Loic Andre Henri, Molteni, Giuseppe   +1 more
openaire   +3 more sources

Sharp inequalities for coherent states and their optimizers

Advanced Nonlinear Studies, 2023
We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group, Lieb and Solovej for SU(2), and Kulikov ...
Frank Rupert L.
doaj   +1 more source

Ulam Stability of Jensen Functional Inequality on a Class of Noncommutative Groups

Journal of Function Spaces, 2023
In the paper, we introduce new ρ-functional inequalities related to the Jensen functional equation and some properties. The Hyers-Ulam stability of functional inequalities is proved.
Gang Lu, Wenlong Sun, Yuanfeng Jin, Qi Liu   +3 more
doaj   +1 more source

On Some Fractional Integral Inequalities Involving Caputo–Fabrizio Integral Operator

Axioms, 2021
In this paper, we deal with the Caputo–Fabrizio fractional integral operator with a nonsingular kernel and establish some new integral inequalities for the Chebyshev functional in the case of synchronous function by employing the fractional integral ...
Vaijanath L. Chinchane, Asha B. Nale, Satish K. Panchal, Christophe Chesneau   +3 more
doaj   +1 more source

Delta-Convexity With Given Weights

Annales Mathematicae Silesianae, 2020
Some differentiability results from the paper of D.Ş. Marinescu & M. Monea [7] on delta-convex mappings, obtained for real functions, are extended for mappings with values in a normed linear space.
Ger Roman
doaj   +1 more source

The logarithmic mean of two convex functionals

Open Mathematics, 2020
The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well.
Raïssouli Mustapha, Furuichi Shigeru
doaj   +1 more source