Let E be a real q-uniformly smooth Banach space, which is also uniformly convex (for example, Lp or p spaces, 1 < p <∞), and C be a nonempty bounded closed convex subset of E. Let T : C→ C be a k-strictly asymptotically pseudocontractive map with a nonempty fixed point set. A hybrid algorithm is constructed to approximate fixed points of such maps. Furthermore, strong convergence of the propose...

Let K be the compositum of a real quadratic number field K2 and a complex cubic number field K3 . Further, let e be a unit of K which is also a relative unit with respect to K/K2 and K/K3. The absolute discriminant of this non-Galois sextic number field K is estimated from above by a simple, strictly increasing, polynomial function of e . This estimate, which can be used to determine a generato...

Let k be a totally real field, and let A/k be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphisms are all defined over k. Then the only strictly compatible families of abstract, absolutely irreducible representations of Gal(k/k) coming from A are tensor products of Tate twists of symmetric powers of two-dimensional λ-adic representations plus field a...

We discuss two facets of the interaction between geometry and algebra in Banach algebras. In class unital algebras, there is essentially one known example which also strictly convex as a space. recall this example, finite-dimensional, consider open question generalising it to infinite dimensions. C*-algebras, we exhibit striking tighter relationship that exists there.

We give an algorithm fr the Computation of K-terminal reliability in planar graphs, whose worst-case complexity is strictly exponential in the square root of the total number of

R c(x)dx = 1. For any sufficiently large number K the space Lp([−K,K]) of all Lp-functions with support in the interval [−K,K] is an invariant space of Wc,α. It is known that Wc,α restricted to Lp([−K,K]) is a compact operator with eigenvalues α−k, k = 0, 1, . . . , and spectrum {α−k : k = 1, 2, . . .} ∪ {0}, which are independent of c and K. This result is better understood in the context of w...