17 research outputs found
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 < s ≤ 1 and ψ an s-convex function, s – ψ -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s – ψ -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 – ψ -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
Properties of some functionals associated with h-concave and quasilinear functions with applications to inequalities
Some extensions of the Marcinkiewicz interpolation theorem in terms of modular inequalities
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> 1 and also a reversed version for 0 < p< 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
On n-th James and Khintchine constants of Banach spaces
For any Banach space X the n-th James constants J(n)(X) and the n-th Khintchine constants K-p,q(n)(X) are investigated and discussed. Some new properties of these constants are presented. The main result is an estimate of the n-th Khintchine constants K-p,q(n)(X) by the n-th James constants Jn (X). In the case of n = 2 and p = q = 2 this estimate is even stronger and improvs an earlier estimate proved by Kato-Maligranda-TakahashiValiderad; 2008; 20080331 (evan)</p