In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.

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∗).

Abstarct: The conventional equilibria problem found in many economics and network models is based on a scalar cost, or a single objective. Recently, equilibria problems based on a vector cost, or multicriteria, have received considerable attention. In this paper, we study a scalarization method for analyzing network equilibria problems with vector-valued cost function. The method is based on th...

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...