On a theorem of Ph. Bénilan concerning semigroups systems
Akira Maruyama · Proceedings of the Japan Academy Series A Mathematical Sciences · 1976
Let X be a real Banach space.By the duality map of X into X*, the dual space o X, we mean the mulivalued mapping F of X into X* defined by Fx={f e X*; (x,f=[Ixl]--llfl]}.The tangen functional v(z, y) on XX is defined by v(x, y)=lim t-(]lx+tyl[-Ilxll) for x, y e X, and it is known that ,(x, y) satisfies the following conditions" (a) r(x, y) _IlYll, (b) v(x, y+y.)_v(x, y)+v(x, y), (c) r(x, ay)=a.v(x,y) for a>0,