Fixed Point Theorems and Duality Theorems for
Wataru Takahashi · 2008
In this article, we first define nonlinear operators wfiich are connected with resolvents of maximal monotone operators in Banach spaces and then prove fixed point theorems for the nonlinear operators in smooth strictly convex and reflexive Banach spaces. Further, we prove duality theorems for two nonlinear mappings in Banach spaces, i.e., a relatively nonexpansive mapping and a generalized nonexpansive mapping. Finally, motivated by such duality theorems, we define nonlinear operators in Banach spaces which are connected with the conditional expectations in the probability theory. Then, we obtain orthgonal properties for the nonlinear operators.