A FAMILY of inequalities concerning inner products of vectors and functions began with Cauchy. The extensions and generalizations later led to the inequalities of Schwarz, Minkowski and Holder. The well known Holder inequality involves the inner product of vectors measured by Minkowski norms. In this paper, another step of extension is taken so that a Holder type inequality may apply to general...

This article is the second and final part of author’s work published in previous issue journal. The main result statement that if for functions (...) , where m 2 numbers p1,...,pm ∈ (1, +∞] are such 1/p1 + ... 1/pm < 1 “non-resonant” condition fulfilled (the concept introduced by author from spaces L^p(R^n), p +∞]), then: (...), [a, b] - n-dimensional parallelepiped, constant C > 0 does n...

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holde...

let = be a non-negative matrix. denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. if we used instead of the purpose of this paper is to establish a hardy type formula for , where is hausdorff matrix and a similar result is also established for where in particular, we apply our results to the cesaro...

We prove a limit theorem connected to graphs, which when the graph is a cycle reduces to Szego's theorem for the trace of a product of Toeplitz matrices. The main tool used is a Holder type inequality for multiple integrals of functions which are applied to variables satisfying linear dependency relations.

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

The a-posteriori error evaluation based on differential approximation of a finite-difference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Largange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic bound...

β1 ψ dx− ab+ α1β1. Young’s inequality [2, 1, 4] states that for every a ∈ [α1, α2] and b ∈ [β1, β2] (2) 0 ≤ F (a, b), where the equality holds iff φ(a) = b (or, equivalently, ψ(b) = a). Among the classical inequalities Young’s inequality is probably the most intuitive. Indeed, its meaning can be easily grasped once the integrals are regarded as areas below and on the left of the graph of φ (see...

The well-known approximation of the difference between the arithmetic average and geometric average returns as one-half of the variance of the underlying returns is reexamined using Jensen’s Inequality. The ”defect” in Jensen’s Indequality, is given an exlicit formula in terms of the variance following some ideas put forward by Holder. A new form of the AM-GM Inequality follows and is is applie...