Results 21 to 30 of about 302 (49)

Nash type inequalities for fractional powers of non-negative self-adjoint operators [PDF]

Transaction of the American Mathematical Society. 359, 7 (2007) 3085-3097, 2004
Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator $A$, we prove a Nash type inequality for the fractional powers $A^{\alpha}$ of $A$. Under some assumptions, we give ultracontractivity bounds for the semigroup $(T_{t,{\alpha}})$ generated by $-A^{\alpha}$.
arxiv   +1 more source

Functional analogs of the Shephard, Busemann-Petty, and Milman problems [PDF]

arXiv, 2022
The paper studies possible functional analogs of classical problems from convex geometry. In particular, we provide some bounds in the functional Shephard, Busemann-Petty, and Milman problems generalizing known bounds in this problems for convex sets.
arxiv  

Stability for the logarithmic Sobolev inequality [PDF]

arXiv, 2023
This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality, with explicit stability constants.
arxiv  

Hermite-Hadamard-type inequalities in the approximate integration [PDF]

Math. Inequal. Appl. 11 (2008), 693-700, 2008
We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.
arxiv   +1 more source

Old and new on the 3-convex functions [PDF]

arXiv, 2023
The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.
arxiv  

Complete positivity order and relative entropy decay

Forum of Mathematics, Sigma
We prove that for a GNS-symmetric quantum Markov semigroup, the complete modified logarithmic Sobolev constant is bounded by the inverse of its complete positivity mixing time.
Li Gao, Marius Junge, Nicholas LaRacuente, Haojian Li   +3 more
doaj   +1 more source

Partitions and functional Santalo inequalities [PDF]

Arch. Math. 92 (1) (2009) 89-94, 2010
We give a direct proof of a functional Santalo inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santalo inequality. The argument combines a logarithmic form of the Prekopa-Leindler inequality and a partition theorem of Yao and Yao.
arxiv   +1 more source

Some new bounds of Chebyshev and Grüss-type functionals on time scales

Applied Mathematics in Science and Engineering
In this work, Korkine and Sonin's identities are defined on arbitrary time scales. These identities are utilized to establish the Chebyshev and Grüss-type inequalities on time scales.
Ammara Nosheen, Khuram Ali Khan, Muhammad Kashif, Rostin Matendo Mabela   +3 more
doaj   +1 more source

Estimating the Hardy Constant of Nonconcave Homogeneous Quasideviation Means

Annales Mathematicae Silesianae
In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely
Páles Zsolt, Pasteczka Paweł
doaj   +1 more source

Some Refinements of Discrete Jensen's Inequality and Some of Its Applications [PDF]

arXiv, 2006
In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting inequalities.
arxiv