Results 101 to 110 of about 5,472,506 (230)

Fixed Points in Functional Inequalities

Journal of Inequalities and Applications, 2008
Using fixed point methods, we prove the generalized Hyers-Ulam stability of the following functional inequalities and in the spirit of Th. M. Rassias stability approach.
Park Choonkil
doaj  

Functional Inequalities for Particle Systems on Polish Spaces

, 2005
Various Poincare-Sobolev type inequalities are studied for a reaction-diffusion model of particle systems on Polish spaces. The systems we consider consist of finite particles which are killed or produced at certain rates, while particles in the system ...
Röckner, Michael, Wang, Feng-Yu
core   +1 more source

Functional inequalities involving special functions II

Journal of Mathematical Analysis and Applications, 2007
The author [J. Math. Anal. Appl. 319, No. 2, 450--459 (2006; Zbl 1091.33002)] has shown for the ratio \(m(s) = F(a,b,a+b,1-r^2)/F(a,b,a+b,r^2)\) of hypergeometric functions, \[ \sqrt{(m(r)m(s))} \leq m(\sqrt{(rs))}, \quad a, b > 0,\quad r, s\in (0,1).
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3-variable Jensen ρ -functional inequalities and equations

, 2016
In this paper, we introduce and investigate Jensen ρ-functional inequalities associated with the following Jensen functional equations f(x+ y + z) + f(x+ y − z)− 2f(x)− 2f(y) = 0, f(x+ y + z)− f(x− y − z)− 2f(y)− 2f(z) = 0.
Gang Lu, Qi Liu, Yuanfeng Jin, Jun Xie
semanticscholar   +1 more source

Functional Inequalities via Lyapunov conditions [PDF]

, 2010
We review here some recent results by the authors, and various coauthors, on (weak,super) Poincar\'e inequalities, transportation-information inequalities or logarithmic Sobolev inequality via a quite simple and efficient technique: Lyapunov ...
Cattiaux, Patrick, Guillin, Arnaud
core   +3 more sources

Spectral and functional inequalities on antisymmetric functions

Ufimskii Matematicheskii Zhurnal
We obtain a number of spectral and functional inequalities related to Schrödinger operators defined on antisymmetric functions. Among them are Lieb - Thirring and CLR inequalities. Besides, we find new constants for the Sobolev and the Gagliardo - Nirenberg inequalities restricted to antisymmetric functions.
Laptev, A. A., Shcherbakov, I. A.
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ON FUNCTIONAL INEQUALITIES FORTHE PSI FUNCTION

Issues of Analysis
In this note we study the monotonicity of the function $x\mapsto (1 +bx)^a/ (1 + ax)^b$. We also give the several inequalities involving the psi function, whic is the logarithmic derivative of the gamma function.
Bhayo, B. A., Xie, L., Yar, Ş. Yildiz
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ADDITIVE rho-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES

, 2015
In this paper, we solve the additive ρ -functional inequalities ‖ f (x+ y)− f (x)− f (y)‖ ∥∥∥ρ ( 2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ (0.1) and ∥∥∥2 f ( x+ y 2 ) − f (x)− f (y) ∥∥∥ ‖ρ ( f (x+ y)− f (x)− f (y))‖ , (0.2) where ρ is a fixed non-Archimedean ...
Choonkill Park
semanticscholar   +1 more source

Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces

, 2015
In this article, we prove the generalized Hyers-Ulam stability of the following Pexider functional inequalities ‖f(x) + g(y) + kh(z)‖ ≤ ∥∥∥∥kp(x+ y k + z )∥∥∥∥ , ‖f(x) + g(y) + h(z)‖ ≤ ∥∥∥∥kp(x+ y + z k )∥∥∥∥ in non-Archimedean Banach spaces. c ©2015 All
Sang Og Kim, A. Bodaghi, Choonkill Park
semanticscholar   +1 more source

Functional equation approach to inequalities, VI

Journal of Mathematical Analysis and Applications, 1980
In connection with the backward Cauchy inequality \[ (a_ 1b_ 1- \sum^{n}_{j=2}a_ jb_ j)^ 2\geq (a^ 2_ 1- \sum^{n}_{j=2}a^ 2_ j)(\quad b^ 2_ 1-\sum^{n}_{j=2}b^ 2_ j) \] (with equality holding if and only if \(b_ j=ca_ j\), where \(a_ j,b_ j\geq 0\), \(1\leq j\leq n\), c is a constant), this paper establishes the Hölder-Lorentz inequality, the Minkowski ...
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