COMMON FIXED POINTS FOR SEMIGROUPS OF POINTWISE LIPSCHITZIAN MAPPINGS IN BANACH SPACES

Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the existence of common fixed points for pointwise Lipschitzian semigroups of nonlinear mappings T-t : C -> C, where each T, is pointwise Lipschitzian. The latter means that there exists a family of functions alpha(t) : C -> [0, infinity) such that parallel to T-t(x)-T-t(y)parallel to <= alpha(t) (x)parallel to x-y parallel to for x, y is an element of C. We also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Frechet derivatives.