We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequalities of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. In parti...

Abstract. By the use of techniques of real analysis and weight functions, we obtain two lemmas and build a few equivalent conditions of a Hardy-type integral inequality with a non-homogeneous kernel, related to a parameter where the constant factor is expressed in terms of the extended Riemann zeta function. Meanwhile, a few equivalent conditions for two kinds of Hardytype integral inequalities...

By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy’s nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocal...

By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy’s nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocal...

By using the methods of real analysis and mid-value theorem, we introduce some lemmas obtain a new reverse extended Hardy–Hilbert’s inequality with two partial sums multi-parameters. We also give few equivalent conditions best possible constant factor related to several parameters in inequality. Some particular inequalities are deduced.

By introducing several independent parameters, according to the structural symmetry of quasi-homogeneous kernels and Hilbert-type inequality, using weight function method, parameter conditions optimal n-multiple series inequality with are discussed, equivalent expression formula best constant factor obtained. As applications, some special symmetric inequalities given.

*Correspondence: [email protected]; [email protected] 2Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, P.R. China Full list of author information is available at the end of the article Abstract By using the way of weight functions and Hadamard’s inequality, a half-discrete Hilbert-type inequality similar to Mulholland’s inequality with a best constant...

Abstract By means of the weight functions, idea introducing parameters and technique real analysis, a new Hardy–Hilbert-type integral inequality with homogeneous kernel $\frac{1}{(x + y)^{\lambda}}\ (\lambda &gt; 0)$ 1(x+y<m...

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals time scale calculus. These extensions used to generalize Hardy-type inequalities with general kernels variables. Some Hardy Hilbert Polya Knop type also discussed as special cases. Classical new deduced from main results using particular scales.

We solve the problem of best approximation closed operators by linear bounded in Hilbert spaces under assumption that operator transforms orthogonal basis space into an system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple is established. also demonstrate application these results concrete situations: powers Laplace-Beltrami on classes functions defined Ri...