A Unified Generalization of Aczél, Popoviciu and Bellman’s Inequalities
نویسنده
چکیده
In this paper, we give a unified generalization of Aczél, Popoviciu and Bellman's inequalities. The result is then applied to deriving a refinement of Aczél's inequality and Bellman's inequality. As consequences, several interesting integral inequalities of Aczél-Popoviciu-Bellman type are obtained.
منابع مشابه
Some generalizations of Aczél, Bellman’s inequalities and related power sums
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...
متن کاملNew generalizations of Popoviciu-type inequalities via new Green’s functions and Montgomery identity
The inequality of Popoviciu, which was improved by Vasić and Stanković (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green's functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green's functions. As an application, we formulate the monotonicity of linear functionals construc...
متن کاملSome functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non- increasing function which is$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ is studied. We show that the exponent $p(.)$ for which these modular ine...
متن کاملA Note on Aczél Type Inequalities
The main result here is a simple general-purpose numerical inequality that can be used to produce a variety of Aczél type inequalities with little effort.
متن کاملOn Generalization of Cebysev Type Inequalities
In this paper, we establish new Cebysev type integral inequalities involving functions whose derivatives belong to L_{p} spaces via certain integral identities.
متن کامل