Let T be a continuous linear map V → V for a (separable) Hilbert space V . Its spectrum σ(T ) is a compact subset of R, so is certainly contained in some finite interval [a, b]. As usual, for a self-adjoint continuous operator S on V , write S ≥ 0 when 〈Sv, v〉 ≥ 0 for all v ∈ V . For self-adjoint S, T , write S ≤ T when T − S ≥ 0. At the outset, with a ≤ −|T |op and b ≥ |T |op, we have, 〈a · v,...

A singular value inequality due to Bhatia and Kittaneh says that if A and B are compact operators on a complex separable Hilbert space such that A is self-adjoint, B 0, and A B; then sj(A) sj(B B) for j = 1; 2; :::We give an equivalent inequality, which states that if A;B; and C are compact operators such that A B B C 0; then sj(B) sj(A C) for j = 1; 2; :::Moreover, we give a sharper inequality...

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multi-valued hemicontractive-type mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algori...

In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The investigated here generalize several known scales and unify extend continuous their corresponding discrete analogues. Our results will be proved by using algebraic inequalities, Hölder inequality, Jensen’s inequality

This paper presents an elastic demand extension of the fixed-demand simultaneous routeand-departure choice dynamic user equilibrium model originally presented in Friesz et al. (1993). Although Friesz et al. (2011) show that analysis and computation of dynamic user equilibrium with constant travel demand is tremendously simplified by stating it as a a differential variational inequality (DVI), t...

In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results known We also get classical Hardy–Hilbert inequality.

Problem 1. Hilbert space and the Riesz representation theorem. If you need help with this, it can be found in lots of places – for instance [1] has a nice treatment. i) A pre-Hilbert space is a vector space V (over C) with a 'positive definite sesquilinear inner product' i.e. a function 1 2 and replace v byˆv = v/v, v 1 2 which hasˆv, ˆ v = 1. Thus we may as well assume v, v = 1. Now using the ...

In 1953, Blumenthal showed that every semi-metric space that is isometrically embeddable in a Hilbert space has the n-point property; we have previously called such spaces supermetric spaces. Although this is a strictly stronger property than triangle inequality, it is nonetheless closely related and many useful metric spaces possess it. These include Euclidean, Cosine and Jensen-Shannon spaces...