Strong converse inequalities for Baskakov operators

We give a strong converse inequality of type B in terms of unified K-functional K_λ^α( f,t²)(0λ1, 0<α<2) for Baskakov operators.     

Strong converse inequalities for Meyer-König and Zeller operators

In this paper we give the strong converse inequality of type B for Meyer-König and Zeller operators.     

Strong converse inequality for Poisson sums

The rate of convergence of Poisson sums and their combinations are shown to be equivalent to appropriate -functionals.

     

Strong converse inequality for Kantorovich polynomials

For the Kantorovich polynomial approximationK _n (f, t), 1<p≤∞, we prove that, for somem, This equivalence includes a strong converse inequality of type B.     

Sharp Marchaud and converse inequalities in Orlicz spaces

For spaces on , and , sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on , and ) for which is convex for some , , where is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

     

广义Baskakov型算子的强逆不等式

利用二阶Ditzian-Totik模考虑一类算子的强逆不等式，这类不等式曾经被许多者用不同的方法研究过。本文将采用一种统一的方法来处理一大类算子的强逆不等式，得到了它们的Ditzian-Ivanov结果。本方法适用于更广的算子。     

STRONG CONVERSE INEQUALITY FOR SZASZ-DURRMEYER OPERATORS

For Szasz-Durrmeyer operators Ln (f,z), 1＜ p≤∞, we prove that, forsome m, w^2φ(f,1/√n)p ≤(≤M(││Ln,f,x) - ,f││p ││Lmn(f, x) -f││p),where φ(x)^2 =x, M ＞0,w^2φ(f,t)p is Ditzian-Totik modulus of smoothness.     

Strong Haagerup inequalities with operator coefficients

We prove a Strong Haagerup inequality with operator coefficients. If for an integer d, denotes the subspace of the von Neumann algebra of a free group F_I spanned by the words of length d in the generators (but not their inverses), then we provide in this paper an explicit upper bound on the norm on , which improves and generalizes previous results by Kemp–Speicher (in the scalar case) and Buchholz and Parcet–Pisier (in the non-holomorphic setting). Namely the norm of an element of the form ∑_{i=(i1,…,id)}a_iλ(g_i1g_id) is less than , where M₀,…,M_d are d+1 different block-matrices naturally constructed from the family (a_i)_iI^d for each decomposition of I^dI^l×I^d−l with l=0,…,d. It is also proved that the same inequality holds for the norms in the associated non-commutative L_p spaces when p is an even integer, pd and when the generators of the free group are more generally replaced by *-free -diagonal operators. In particular it applies to the case of free circular operators. We also get inequalities for the non-holomorphic case, with a rate of growth of order d+1 as for the classical Haagerup inequality. The proof is of combinatorial nature and is based on the definition and study of a symmetrization process for partitions.     

Strong convergence results for hemivariational inequalities

The purpose of this paper is to study a regularization method of solutions of ill-posed problems involving hemivariational inequalities in Banach spaces. Under the assumption that the hemivariational inequality is solvable, a strongly convergent approximation procedure is designed by means of the so-called Browder-Tikhonov regularization method. Our results generalize and extend the previously known theorems.     

Strong vector variational inequalities in Banach spaces

In this work, we study some existence results for solutions for a class of strong vector variational inequalities (for short, SVVI) in Banach spaces. The solvability of the SVVI without monotonicity is presented by using the fixed point theorems of Brouwer and Browder, respectively. The solvability of the SVVI with monotonicity is also proved by using the Ky Fan lemma. Our results give a positive answer to an open problem proposed by Chen and Hou.     

Strong convergence result for monotone variational inequalities

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of subgradient extra-gradient method and viscosity approximation method with adoption of Armijo-like step size rule in infinite dimensional real Hilbert spaces. Our results are obtained under mild conditions on the iterative parameters. We apply our result to nonlinear Hammerstein integral equations and finally provide some numerical experiments to illustrate our proposed algorithm.     

Strong inequalities for capacitated survivable network design problems

We present several classes of facet-defining inequalities to strengthen polyhedra arising as subsystems of network design problems with survivability constraints. These problems typically involve assigning capacities to a network with multicommodity demands, such that after a vertex- or edge-deletion at least some prescribed fraction of each demand can be routed. Received: December 1997 / Accepted: April 2000?Published online September 20, 2000     

Strong valid inequalities for Boolean logical pattern generation

0–1 multilinear programming (MP) captures the essence of pattern generation in logical analysis of data (LAD). This paper utilizes graph theoretic analysis of data to discover useful neighborhood properties among data for data reduction and multi-term linearization of the common constraint of an MP pattern generation model in a small number of stronger valid inequalities. This means that, with a systematic way to more efficiently generating Boolean logical patterns, LAD can be used for more effective analysis of data in practice. Mathematical properties and the utility of the new valid inequalities are illustrated on small examples and demonstrated through extensive experiments on 12 real-life data mining datasets.     

Strong summability of multiple Fourier series and Sidon-type inequalities

We study different versions of strong summation of N-dimensional Fourier series over polyhedrons and related estimates for integral norms of linear means of the Dirichlet kernels (Sidon-type inequalities). Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1630–1635, December, 1998.     

A converse to the Jensen inequality,its matrix extensions and inequalities for minors and eigenvalues

We obtain a scalar inequality, converse to the Jensen inequality. We also derive an operator converse to the Jensen inequality. As special cases, we obtain inequalities, similar to the Kantorovich one as well as some operator generalizations of them. Using some exterior algebra, we prove a generalization of the Sylvester determinant theorem. We also deduce some determinant analogs of the additive and multiplicative Kantorovich inequalities.     

Strong valid inequalities for orthogonal disjunctions and bilinear covering sets

In this paper, we derive a closed-form characterization of the convex hull of a generic nonlinear set, when this convex hull is completely determined by orthogonal restrictions of the original set. Although the tools used in this construction include disjunctive programming and convex extensions, our characterization does not introduce additional variables. We develop and apply a toolbox of results to check the technical assumptions under which this convexification tool can be employed. We demonstrate its applicability in integer programming by providing an alternate derivation of the split cut for mixed-integer polyhedral sets and finding the convex hull of certain mixed/pure-integer bilinear sets. We then extend the utility of the convexification tool to relaxing nonconvex inequalities, which are not naturally disjunctive, by providing sufficient conditions for establishing the convex extension property over the non-negative orthant. We illustrate the utility of this result by deriving the convex hull of a continuous bilinear covering set over the non-negative orthant. Although we illustrate our results primarily on bilinear covering sets, they also apply to more general polynomial covering sets for which they yield new tight relaxations.     

Strong convergence result for solving monotone variational inequalities in Hilbert space

Numerical Algorithms - In this paper, we study strong convergence of the algorithm for solving classical variational inequalities problem with Lipschitz-continuous and monotone mapping in real...     

Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a variational inequality in a Banach space. Our results extend and improve the recent ones announced by Li (J Math Anal Appl 295:115–126, 2004), Jianghua (J Math Anal Appl 337:1041–1047, 2008), and many others.