No abstract uploaded!

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of slowing down the twisting in the mean gives rise to a non-empty discrete spectrum

Let and be a real -uniformly smooth Banach space, be a nonempty closed convex subset of and be a Lipschitz continuous mapping. Let and be bounded sequences in and and be real sequences in satisfying some restrictions. Let be the sequence generated from an arbitrary by the Ishikawa iteration process with errors: , , . Sufficient and necessary conditions for the strong convergence to a fixed point of is established.

Let A be a A -algebra with real rank zero. Let A and A be Hilbert A -modules with A being full. Suppose that A is a linear map preserving orthogonality, ie,

The purpose of this paper is to construct two superimposed optimization methods for solving the mixed equilibrium problem and variational inclusion. We show that the proposed superimposed methods converge strongly to a solution of some optimization problem. Note that our methods do not involve any projection.