In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space R and vector-valued functions in a weakly compact subset of a Banach vector space generated by m Lμ-spaces for 1 ≤ p < +∞. Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach...

has the unit circle as its graph, but these equations do not represent the same curve— because the circle is traced out in different ways on the graphs. Be sure you see the distinction between the vector-valued function and the real-valued functions and All are functions of the real variable but is a vector, whereas and are real numbers for each specific value of . Vector-valued functions serve...

This paper extends the theory of Zen spaces (weighted Hardy/Bergman on right-hand half-plane) to Hilbert-space valued case, and describes multipliers them; it is shown that methods H∞ control can therefore be extended certain weighted L2 input output spaces. Next, case retarded delay systems with operator-valued transfer functions analysed, dependence structure determined by developing an exten...

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces proved that a complete space, whose all closed bounded subsets are compact, mapping has fixed point. This article presents generalizations above results by omitting assumption compact.

It is useful to treat real-valued functions (or complex-valued functions, or vector space-valued functions) as elements of a vector space, so that the tools from linear algebra can be applied. Given a set X one may consider the vector space R of all real-valued functions with domain X. If X is finite, say with n elements, then this is just the familiar vector space R. The more interesting examp...

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...