The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on R is proved. Similar results have been recently obtained for the Jacobi weight on [−1, 1] and for the generalized Laguerre weight on [0,+∞). Numerical construction of the Gauss–Hermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few n...

We study integration in a class of Hilbert spaces of analytic functions defined on the Rs. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite integration rules and show that the errors of our algorithms decay exponentially fast. Furthermore, we study tractability in terms of s and log ε−1 and give necessary and sufficie...

Keywords: Hermite–Hadamard inequalities Jensen's inequality Xiao–Srivastava–Zhang–Pečarić–Svrtan–Jensen type inequalities Refinements and extensions Convex functions a b s t r a c t The main object of this paper is to give several refinements and extensions of the Hermite–Hadamard and Jensen inequalities in n variables. Relevant connections of the results presented here and the various inequali...

In this paper the inverse resonance problem for the Hermite operator is investigated. The Hermite operator H = a + a∗ + b with the creation operator a, the annihilation operator a∗, and a finitely supported multiplication operator b, is an unbounded operator on `(N0) having finitely many eigenvalues and infinitely many resonances (except for b = 0 when there are no eigenvalues or resonances). I...

We give a short introduction to Padé approximation (rational approximation to a function with close contact at one point) and to Hermite-Padé approximation (simultaneous rational approximation to several functions with close contact at one point) and show how orthogonality plays a crucial role. We give some insight into how logarithmic potential theory helps in describing the asymptotic behavio...

The fuzzy-number valued up and down λ-convex mapping is originally proposed as an intriguing generalization of the convex mappings. newly suggested mappings are then used to create certain Hermite–Hadamard- Pachpatte-type integral fuzzy inclusion relations in fractional calculus. It also revise Hermite–Hadamard inclusions with regard (U∙D F-N∙V∙Ms). Moreover, Hermite–Hadamard–Fejér has been pro...

The following is the classical Hermite-Hadamard inequality [4, 5]: f ( a+ b 2 ) ≤ 1 b− a (S) ∫ b a f(x)dμ ≤ f(a) + f(b) 2 . which provides estimates of the mean value of a convex function f on [a, b] where μ is the Lebesgue measure on R. This inequality in general, is not valid in the fuzzy context. In this paper, we find necessary and sufficient conditions of Hermite-Hadamard type inequality f...

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faste...

Moments are widely used in pattern recognition, image processing, and computer vision and multi resolution analysis. In this paper, we first printout Gaussian-Hermite moments, and propose a new method to extract the object’s features based on Gaussian-Hermite moments. Following, for training ART neural network, the moment features were inputted to ART as its parameters; so that, a classifier wa...

A modification of iris recognition algorithm using Hermite transform to find iris key points has been developed. The iris image mask for the areas free of eyelids, eyelashes and glares is constructed. The key points are found inside the masked iris region. The use of eye rotation compensation based on Polar Hermite Transform before iris parameterization makes the method more effective. The prop...