let $x$ be a reflexive banach space, $t:xto x$ be a nonexpansive mapping with $c=fix(t)neqemptyset$ and $f:xto x$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. in this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences t...

We show that transport inequalities, similar to the one derived by Talagrand [30] for the Gaussian measure, are implied by logarithmic Sobolev inequalities. Conversely, Talagrand’s inequality implies a logarithmic Sobolev inequality if the density of the measure is approximately log-concave, in a precise sense. All constants are independent of the dimension, and optimal in certain cases. The pr...

We establish new functional versions of the Blaschke-Santaló inequality on the volume product of a convex body which generalize to the nonsymmetric setting an inequality of K. Ball [2] and we give a simple proof of the case of equality. As a corollary, we get some inequalities for logconcave functions and Legendre transforms which extend the recent result of Artstein, Klartag and Milman [1], wi...

with equality if and only if the sequences ai and bi are proportional. The Aczél inequality (1) plays an important role in the theory of functional equations in non-Euclidean geometry. During the past years, many authors have given considerable attention to this inequality, its generalizations and applications [2-11]. As an example, the Hölder-like generalization of the Aczél inequality (1), de...

This paper provides a critical review of the recent literature on inequality and growth. After discussing historical and more recent distributional trends as well as empirical evidence on the relationship between inequality and growth, I focus on recent explanations of the inequality-growth puzzle. I consider both the impact of the functional and the personal distribution on long-run growth rat...

In this note we give a completely different proof to a functional inequality established by Ismail and Laforgia for the survival function of the gamma distribution and we show that the inequality in the question is in fact the so-called new-is-better-than-used property, which arises in economic theory. Moreover, we extend this result to arbitrary reliability functions and we present a new simpl...

Boundedness properties of semigroups are studied by using general PoincaréSobolev type inequalities, from which Gross’ theorem on hyperboundedness and log-Sobolev inequality is extended. Some results hold also for nonsymmetric semigroups. For instance, a super-Poincaré inequality always imply an estimate of the corresponding semigroup. In particular, the log-Sobolev inequality implies the hyper...

This paper deals with the uniqueness and stability problem for uncertain bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional approach and free-weighting matrices method, new delay-dependent stability criteria with two classes of system uncertainties are presented in terms of linear matrix inequalities (LMIs). By using the ...