in this paper, we introduce the idea of relative order and type of entire functions represented by banach valued dirichlet series of two complex variables to generalize some earlier results.proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by dirichlet series is the same as that of it...

We prove existence and uniqueness of strong generalized entropy solution to the Cauchy problem for an infinite dimensional system of Keyfitz-Kranzer type, in which the unknown vector takes its value in an arbitrary Banach space. We study the Cauchy problem for an equation ut + (φ(‖u‖)u)x = 0 (1) with initial condition u(0, x) = u0(x). (2) Here the unknown vector u = u(t, x) is defined in a half...

We combine methods from convex analysis, based on a function of Simon Fitzpatrick, with a fine recent idea due to Voisei, to prove maximality of the sum of two maximal monotone operators in Banach space under various natural transversality conditions.

The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subse...

We study the complexity of Banach space valued integration. The input data are assumed to be r-smooth. We consider both definite and indefinite integration and analyse the deterministic and the randomized setting. We develop algorithms, estimate their error, and prove lower bounds. In the randomized setting the optimal convergence rate turns out to be related to the geometry of the underlying B...

We will use Garcı́a-Falset and Lloréns Fuster’s paper on the AMC-property to prove that a Banach space X that 1 δ embeds in a subspace Xδ of a Banach space Y with a 1-unconditional basis has the property AMC and thus the weak fixed point property. We will apply this to some results by Cowell and Kalton to prove that every reflexive real Banach space with the property WORTH and its dual have the ...

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality probl...

A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the ...

Then Xc is the completion of {X, \\ \\c). Alternatively || ||c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X —> Z into a Banach space extends with preservation of norm to an operator L\XC —» Z. The Banach envelope of / (0 < p < 1) is, of course, lx. In 1969, Duren, Romberg and Shields [3] identified the dual space of H_...

Let x be a sequence of real numbers and let p be a real number. The functor x yielding a sequence of real numbers is defined as follows: (Def. 1) For every natural number n holds x(n) = |x(n)|. Let p be a real number. Let us assume that p ≥ 1. The functor l yielding a non empty subset of the carrier of the linear space of real sequences is defined as follows: (Def. 2) For every set x holds x ∈ ...