A Generalization of Kemperman’s Functional Inequality 2f(x) ≤ f(x + h) + f(x + 2h)

1983 ◽  
pp. 281-293
Author(s):  
M. Laczkovich
Keyword(s):  
Functional Inequality

scholarly journals On Gromov's theorem andL 2-Hodge decomposition

2004 ◽  
Vol 2004 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Fu-Zhou Gong ◽  
Feng-Yu Wang
Keyword(s):  
Essential Spectrum ◽  
Vector Bundles ◽  
Functional Inequality ◽  
Upper Bounds ◽  
Hodge Decomposition ◽  
Laplace Type

Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplace-type operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the correspondingL 2-harmonic sections. In particular, some known results concerning Gromov's theorem and theL 2-Hodge decomposition are considerably improved.

A FUNCTIONAL INEQUALITY FOR THE GAMMA FUNCTION

2013 ◽  
Vol 11 (02) ◽  
pp. 1350010
Author(s):  
HORST ALZER
Keyword(s):  
Gamma Function ◽  
Functional Inequality ◽  
Real Numbers ◽  
Positive Real ◽  
Euler’S Constant ◽  
Euler's Constant

Let α and β be real numbers. We prove that the functional inequality [Formula: see text] holds for all positive real numbers x and y if and only if [Formula: see text] Here, γ denotes Euler's constant.

On an Exponential Functional Inequality and its Distributional Version

2015 ◽  
Vol 58 (1) ◽  
pp. 30-43 ◽  
Author(s):  
Jaeyoung Chung
Keyword(s):  
Functional Equation ◽  
Tensor Product ◽  
Functional Inequality ◽  
Schwartz Distribution ◽  
Exponential Functional ◽  
The Stability

AbstractLet G be a group and 𝕂 = ℂ or ℝ. In this article, as a generalization of the result of Albert and Baker, we investigate the behavior of bounded and unbounded functions f : G → 𝕂 satisfying the inequalityWhere ϕ: Gn-1 → [0,∞]. Also as a a distributional version of the above inequality we consider the stability of the functional equationwhere u is a Schwartz distribution or Gelfand hyperfunction, o and ⊗ are the pullback and tensor product of distributions, respectively, and S(x1, ..., xn) = x1 + · · · + xn.

scholarly journals STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN PROPER CQ*-ALGEBRAS

2011 ◽  
Vol 48 (4) ◽  
pp. 853-871 ◽  
Author(s):  
Jung-Rye Lee ◽  
Choon-Kil Park ◽  
Dong-Yun Shin
Keyword(s):  
Functional Inequality ◽  
Additive Functional ◽  
Additive Functional Inequality

scholarly journals Hlawka’s functional inequality

2012 ◽  
Vol 87 (1-2) ◽  
pp. 71-87 ◽  
Author(s):  
Włodzimierz Fechner
Keyword(s):  
Functional Inequality

A maternal factor affecting mouse blastocyst formation

Development ◽  
1994 ◽  
Vol 120 (4) ◽  
pp. 797-802 ◽  
Author(s):  
J.P. Renard ◽  
P. Baldacci ◽  
V. Richoux-Duranthon ◽  
S. Pournin ◽  
C. Babinet
Keyword(s):  
Direct Evidence ◽  
Normal Development ◽  
Functional Inequality ◽  
Preimplantation Embryos ◽  
Mouse Blastocyst ◽  
Maternal Control ◽  
Paternal Genome ◽  
Functional Differences ◽  
Embryonic Genome ◽  
Parental Contribution

Normal development of the mouse embryo requires the presence of both paternal and maternal genomes. This is due to functional differences having their origin in a differential imprinting of parental genomes. Furthermore, several lines of evidence show that the very early interactions between egg cytoplasm and pronuclei may influence the programming of the embryonic genome and modulate the functional inequality of the parental contribution even during preimplantation stages. In this paper, we show that a factor present in ovulated oocytes of the mouse mutant strain DDK and therefore of maternal origin prevents the formation of the blastocyst. This factor, which acts via an interaction with the paternal genome, is present in oocytes as an RNA and is still active in preimplantation embryos. This is the first direct evidence of such a maternal control in the mouse.

scholarly journals Functional Inequalities Associated with Additive Mappings

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Jaiok Roh ◽  
Ick-Soon Chang
Keyword(s):  
Banach Space ◽  
Functional Inequality ◽  
Functional Inequalities ◽  
Stability Theorems ◽  
Group Divisible ◽  
Additive Mappings

The functional inequality‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ  (x,y,z) (x,y,z∈G)is investigated, whereGis a group divisible by2,f:G→Xandϕ:G3→[0,∞)are mappings, andXis a Banach space. The main result of the paper states that the assumptions above together with (1)ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G)and (2)limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, orlimn→∞2nϕ(x/2n−1,y/2n,z/2n)=0  (x,y,z∈G), imply thatfis additive. In addition, some stability theorems are proved.

scholarly journals ADDITIVE FUNCTIONAL INEQUALITIES AND DERIVATIONS ON HILBERT C*-MODULES

2013 ◽  
Vol 55 (2) ◽  
pp. 341-348 ◽  
Author(s):  
FRIDOUN MORADLOU
Keyword(s):  
Banach Spaces ◽  
Functional Inequality ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Formula Group ◽  
Image Position

AbstractIn this paper we investigate the following functional inequality $ \begin{eqnarray*} \| f(x-y-z) - f(x-y+z) + f(y) +f(z)\| \leq \|f(x+y-z) - f(x)\| \end{eqnarray*}$ in Banach spaces, and employing the above inequality we prove the generalized Hyers–Ulam stability of derivations in Hilbert C*-modules.

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