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

Source abstract

Abstract 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 t is pointwise Lipschitzian. The latter means that there exists a family of functions α t : C →[0, ∞ ) such that $\|T_t(x)-T_t(y)\| \leq \alpha _{t}(x)\|x-y\|$ for x , y ∈ C . We also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Fréchet derivatives.