Fixed point and ergodic theorems for nonexpansive mappings on ultrametric Banach spaces.

摘要

Let ( E , ∥ · ∥) be an ultrametric Banach space over a complete ultrametric field ( K , | · |), and let T : E E be a nonexpansive mapping (possibly nonlinear). This dissertation provides fixed-point and ergodic theorems related to T. In particular, we introduce and examine conditions for which the Cesaro-like means: Fnx:=1Pn k=1na kTkx,x∈E, converges both strongly and weakly to a fixed point y of T, where Pn = alpha 1+···+alphan with akk ∈N⊂K being a sequence of nonzero elements satisfying some additional assumptions. We also illustrate our main results by several examples.