Abstract :
We obtain new results on A-properness of sums of dissipative and ball-condensing
maps in p1-Banach spaces. The maps involved need not be self-maps, and
the dissipative maps are not required to satisfy any extra range conditions.
Moreover, the domains of the maps may be closed subsets. It is known that, in
general, it is difficult to prove A-properness at all points of the whole space for a
map defined on a closed subset. An open question on A-properness of a k-contraction
defined on a ball in a general p1-Banach space, raised by Petryshyn in 1975
and 1993, has not been completely solved so far. Our result will give a partial
answer to the open question. New fixed point theorems for sums of the above maps
and range results for dissipative maps are derived. An application to eigenvalue
problems for homogeneous integral equations is provided
