On a Refinement of Hardy-Hilbert's Inequality and Its Applications

In this paper, by introducting a weight coefficient of the form: π/sin(π/r)-1/10(2n+1)1+1/r (r＞1, n∈N0), Hardy-Hilbert's inequality is refined. As its applications, an equivalent Hard y-Hilbert's type inequality and its strengthened form are given, and Hardy-Li ttlewood's inequality is generalized and improved.

AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS

In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.

On Hardy-Hilbert's Integral Inequality and Its Equivalent Form

In this paper, by introducing three parameters a, b and λ, we give some new generalizations of Hardy-Hilbert’s integral inequality. As applications, we con-sider its equivalent form and some particular results.

An Extended Multiple Hardy-Hilbert's Integral Inequality

In this paper, by introducing the norm ｜｜x｜｜ （x ∈ Rn）, a multiple Hardy- Hilbert＇s integral inequality with the best constant factor and it＇s equivalent form are given.

DOUBLE Φ-FUNCTION INEQUALITY FOR NONNEGATIVE SUBMARTINGALES

The authors establish a kind of inequalities for nonnegative submartingales which depend on two functions ψ and ψ, and obtain the equivalent conditions for Φ and ψ such that this kind of inequalities holds. In the caseΦ=ψ ε△2, it is proved that this necessary and sufficient condition is equivalent to qΦ >1.

Discrete Hardy-Hilbert's Inequalities in R^n

By using some auxiliary functions and introducing relative Lemmas, we establish multidimensional discrete Hardy-Hilbert’s inequalities.

Existence theorems of solution to variational inequality problems

This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for the existence of a solution to the problem. This condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. Sufficient solution conditions for a class of nonlinear complementarity problems with P0 mappings are also obtained.

A Survey of Various Refinements and Generalizations of Hilbert's Inequalities

Expounded in this survey article is a series of refinements and generalizations of Hilbert's inequalities mostly published during the years 1990 through 2002.Those inequalities concerned may be classified into several types (discrete and integral etc.), and various related results obtained respectively by L. C. Hsu, M. Z. Gao, B. C. Yang, J. C. Kuang, Hu Ke and H. Hong et.al are described a little more precisely. Moreover, earlier and recent extensions of Hilbert-type inequalities are also stated for reference. And the new trend and the research ways are also brought forward.

Hom-derivations in C^*-ternary Algebras

In this paper,we introduce and solve the following additive(ρ1,ρ2)-functional inequalities‖f(x+y+z)-f(x)-f(y)-f(z)‖≤‖ρ1(f(x+z)-f(x)-f(z))‖+‖ρ2(f(y+z)-f(y)-f(z))‖,whereρ1 andρ2 are fixed nonzero complex numbers with|ρ1|+|ρ2|<2.Using the fixed point method and the direct method,we prove the Hyers–Ulam stability of the above additive(ρ1,ρ2)-functional inequality in complex Banach spaces.Furthermore,we prove the Hyers–Ulam stability of hom-derivations in C^*-ternary algebras.