ON THE FIXED POINT THEOREM OF CONE EXPANSION AND COMPRESSION

Let P be a cone in a real Banach space E. Let s={x|||x||=r}, S={x|||x||=R}, T={x|r<||x||<R} and T={x|r≤||x||≤R}(R>r>0). The fixed point theorem about the expansion and compression of a cone can be formulated as follows.