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# Theorems of Leray-Schauder Type for Accretive Maps

DOI link for Theorems of Leray-Schauder Type for Accretive Maps

Theorems of Leray-Schauder Type for Accretive Maps book

# Theorems of Leray-Schauder Type for Accretive Maps

DOI link for Theorems of Leray-Schauder Type for Accretive Maps

Theorems of Leray-Schauder Type for Accretive Maps book

## ABSTRACT

The following properties are simple consequences of the definitions (see [[32], Proposition 13. l]):

2) (X, y)- 5 (X, y)+ with equality if and only if X* is strictly convex;

where D-4 (L) = lim suphio+ h-' (4 (t) - 4 (t - h)) . A map F : D C X -+ X, is said to be accretive if

(F (x ) - F(Y) X - Y)+ 2 0 for all X, y E D, strongly accretive if there exists c > 0 such that

> c ~ x - y / ~ fora l lx , Y E D (F (4 - F (Y) , X - Y), - and $-accretive if

$(O)=O, $(r) > O f o r r > O and liminf$(r) >O. r+oo

In particular, if (X, ( . , . )) is a Ailbert space, the duality map is the identity map of X , the semi-inner products ( . , . )- and ( . , . )+ coincide with the inner product ( . , . ) of X and the accretive and strongly accretive maps are the so called monotone and strongly monotone maps, respectively.