The disturbance of vector-valued doubly-periodic Riemann boundary-valued problems

Lower semicontinuity for parametric set-valued vector equilibrium-like problems

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

AMENABILITY OF VECTOR VALUED GROUP ALGEBRAS

The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

Computational problems for vector-valued quadratic forms

For R-vector spaces U and V we consider a symmetric bilinear map B : U×U → V . This then defines a quadratic map QB : U → V by QB(u) = B(u, u). Corresponding to each λ ∈ V ∗ is a R-valued quadratic form λQB on U defined by λQB(u) = λ · QB(u). B is definite if there exists λ ∈ V ∗ so that λQB is positive-definite. B is indefinite if for each λ ∈ V ∗, λQB is neither positive nor negative-semidefi...

Vector-valued Laplace Transforms and Cauchy Problems

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are stu...

Parametric Set-Valued Vector Quasi-Equilibrium Problems