More results on a functional generalization of the Cauchy-Schwarz inequality
نویسندگان
چکیده
play an important role in different branches of modernmathematics such as Hilbert space theory, classical real and complex analysis, numerical analysis, probability and statistics, qualitative theory of differential equations and their applications. To date, a large number of generalizations and refinements of the inequalities () and () have been investigated in the literature, e.g., [–]. Recently in [], we have presented a functional generalization of the CauchyBunyakovsky-Schwarz inequality for both discrete and continuous cases as follows.
منابع مشابه
Some 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 کاملSchwarz boundary problem on a triangle
In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...
متن کاملA Generalization of the Cauchy-Schwarz Inequality with Eight Free Parameters
The results of the recent published paper by Masjed-Jamei et al. 2009 are extended to a larger class and some of subclasses are studied in the sequel. In other words, we generalize the well known Cauchy-Schwarz and Cauchy-Bunyakovsky inequalities having eight free parameters and then introduce some of their interesting subclasses.
متن کاملGeneralizations of Cauchy-schwarz in Probability Theory
We explore two generalizations of the Cauchy-Schwarz Bessel’s inequality and the Selberg inequality and their application to probability theory. We then give a tautological proof of the De Caen-Selberg Inequality and a proof of the second Borel-Cantelli Lemma with negative dependence. We finish with a suggestion of how linear operator theory can help us understand the tightness of many Selberg-...
متن کاملA Generalized Cauchy–schwarz Inequality
In the course of realizing certain triangle centers as points that minimize certain quantities, C. Kimberling and P. Moses, in Math. Mag. 85 (2012) 221–227, discovered an inequality in three variables that generalizes the Cauchy-Schwarz inequality, and made a conjecture regarding a generalization of that inequality to an arbitrary number of variables. In this paper, we give a proof of a stronge...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012