Unified treatment of fractional integral inequalities via linear functionals

In the paper we prove several inequalities involving two isotonic linear functionals. We consider inequalities for functions with variable bounds, for Lipschitz and H\" older type functions etc. These results give us an elegant method for obtaining a number of inequalities for various kinds of fractional integral operators such as for the Riemann-Liouville fractional integral operator, the Hadamard fractional integral operator, fractional hyperqeometric integral and corresponding q-integrals

Generalized quasi-Banach sequence spaces and measures of noncompactness

Given 0 &lt; s &#8804; 1 and &#968; an s-convex function, s &#8211; &#968; -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s &#8211; &#968; -spaces. For these spaces, new measures of noncompactness are also defined, related to the Hausdorff measure of noncompactness. As an application, compact sets in s &#8211; &#968; -interpolation spaces of a quasi-Banach couple are studied.Dado 0 < s ? 1 e uma função s-convexa ?, os espaços de sequencias s – ? são introduzidos. Vários espaços quase-Banach de sequencias são assim caracterizados como um caso particular dos espaços s – ?. Para esses espaços novas medidas de não compacidade são também definidas, relacionadas a medida de não compacidade de Hausdorff. Como uma aplicação, conjuntos compactos nos espa, cos de interpolação s – ?, de um par quase-Banach são estudados.44345

Polarization properties of self-diffraction in sillenite crystals: reflection volume gratings

International audienceWe study two-beam interaction in photorefractive sillenite crystals in reflection geometry and derive analytic expressions for the signal gain and its polarization direction in the presence of a strong pump beam. The crystal is cut normal to one of the crystallographic axes, and no external electric field is applied. Crystal absorption and its natural optical activity are taken into account. The coupling effects are strongly dependent on the polarization directions of the interacting beams. We determine the optimal polarization directions and optimal crystal thickness that give maximum signal gain. Experimental results are in excellent agreement with theoretical calculations

A new look at classical inequalities involving Banach lattice norms

Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classical situation). The main aim of this paper is to initiate a more consequent study of classical inequalities in this more general frame. We already here contribute by discussing some results of this type and also by deriving some new results related to classical Popoviciu’s, Bellman’s and Beckenbach-Dresher’s inequalitie

Some new refinements of the Young, Hölder, and Minkowski inequalities

We prove and discuss some new refined Hölder inequalities for any p&gt; 1 and also a reversed version for 0 &lt; p&lt; 1. The key is to use the concepts of superquadraticity, strong convexity, and to first prove the corresponding refinements of the Young and reversed Young inequalities. Refinements of the Minkowski and reversed Minkowski inequalities are also given.

Continuous refinements of some Jensen-type inequalities via strong convexity with applications

In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite-Hadamard, Holder, and Popoviciu type inequalities. As particular cases we point out the corresponding results for sums and integrals showing that our results contain both several well-known but also some new results for these special cases