- Volume 26 Issue 2
Recently many authors [2,3,5,6] proved the existence of zeros of accretive operators and estimated the range of m-accretive operators or compact perturbations of m-accretive operators more sharply. Their results could be obtained from differential equations in Banach spaces or iteration methods or Leray-Schauder degree theory. On the other hand Kirk and Schonberg  used the domain invariance theorem of Deimling  to prove some general minimum principles for continuous accretive operators. Kirk and Schonberg  also obtained the range of m-accretive operators (multi-valued and without any continuity assumption) and the implications of an equivalent boundary conditions. Their fundamental tool of proofs is based on a precise analysis of the orbit of resolvents of m-accretive operator at a specified point in its domain. In this paper we obtain a sufficient condition for m-accretive operators to have a zero. From this we derive Theorem 1 of Kirk and Schonberg  and some results of Morales [12, 13] and Torrejon. And we further generalize Theorem 5 of Browder  by using Theorem 3 of Kirk and Schonberg .