This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...

In this paper, which is the sequel to [GN04a], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually incoherent bases introduced by Donoho and Huo. The Bernstein inequality obta...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

We introduce a projection-type algorithm for solving monotone variational inequality problems in real Hilbert spaces. We prove that the whole sequence of iterates converges strongly to a solution of the variational inequality. The method uses only two projections onto the feasible set in each iteration in contrast to other strongly convergent algorithms which either require plenty of projection...

begin{abstract} In this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. The results present...

Abstract We discuss when an operator T, subject to a rather general inequality in hereditary form, admits unitarily equivalent functional model of Agler type the reproducing kernel Hilbert space associated inequality. The need not be Nevanlinna-Pick type. define defect D our context and structure spectrum T is finite rank. As second application, some consequences concerning ergodic behavior are...

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.