No abstract

We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework ofCAT(0)spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.

Under new hypotheses, and using the Lyapunov-Schmidt reduction, we study the branches of bifurcation of a nonlinear equation of the type u Lu C G. ; u/ D 0, in a neighborhood W of a particular solution. 0 ; 0/ 2 R X, where X is a real Banach space, L a noncompact linear operator defines on X and G is a nonlinear operator defined on W to values in X. This type of bifurcation problems (bifurcation from the trivial branch) have different applications such as resolution of differential equations as those of Von-Karmann and Navier-Stokes or to integral equations as the Urysohn's one.