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...

We present results for pseudodifferential operators on Rd whose symbol a(·,ξ) is almost periodic (a.p.) for each ξ ∈ Rd and belongs to a Hörmander class Sm ρ,δ. We study a linear transformation a 7→ U(a) from a symbol a(x,ξ) to a frequency-dependent matrix U(a)(ξ)λ,λ′ , indexed by (λ,λ′) ∈ Λ×Λ where Λ is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential ope...

for entire functions, the notions of their growth indicators such as ritt order are classical in complex analysis. but the concepts of relative ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. therefore the studies of the growths of entire functions in the light of thei...

a new class of nonlinear set-valued variationalinclusions involving $(a,eta)$-monotone mappings in a banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(a,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

We present a new framework for the hierarchical segmentation of color images. The proposed scheme comprises a nonlinear scale-space with vector-valued gradient watersheds. Our aim is to produce a meaningful hierarchy among the objects in the image using three image components of distinct perceptual significance for a human observer, namely strong edges, smooth segments and detailed segments. Th...

Let a a1, a2, . . . , am ∈ C be an m-dimensional vector. Then, it can be identified with an m ×m circulant matrix. By using the theory of matrix-valued wavelet analysis Walden and Serroukh, 2002 , we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions ar...

The aim of this paper is to introduce the notion Perov–Ćirić–Prešić-type Θ-contractions and obtain some generalized fixed point theorems in setting vector-valued metric spaces. We derive results as consequences our main results. A nontrivial example also provided support validity established As an application, we investigate solution a semilinear operator system Banach space.