in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

Abstract By the use of weight coefficients, idea introduced parameters and technique real analysis, a more accurate Hilbert-type inequality in whole plane with general homogeneous kernel is given, which an extension Hardy–Hilbert’s inequality. An equivalent form obtained. The statements best possible constant factor related to several parameters, operator expressions few particular cases are co...

The hybrid steepest-descent method introduced by Yamada 2001 is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and applicable to a broad range of convexly constrained nonlinear inverse problems in real Hilbert spaces. Lehdili and Moudafi 1996 introduced the new prox-Tikhonov regularization method for proximal point algorithm to genera...

In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial differential mean value theorem, a new weighted containing two sums can be proven, which is further generalization an existing result. Based on obtained results, provide equivalent statements best possibl...

Making use of weight coefficients as well real/complex analytic methods, an extension a Hardy–Hilbert-type inequality with best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression the norm, few particular cases are also considered.

In this paper, by the application of methods of weight functions and the use of analytic techniques, a multidimensional more accurate half-discrete Hilbert-type inequality with the kernel of the hyperbolic cotangent function is proved. We show that the constant factor related to the Riemann zeta function is the best possible. Equivalent forms as well as operator expressions are also investigated.

By using the methods of weight functions and Hermite-Hadamard’s inequality, two kinds of more accurate equivalent reverse multidimensional half-discrete Hilbert-type inequalities with the kernel of hyperbolic cotangent function are given. The constant factor related to the Riemann zeta function is proved to be the best possible. Mathematics subject classification (2010): 26D15, 47A07, 37A10.