The central result in the theory of semigroups of linear operators is the characterization, by the Hille-Yosida theorem, of the generators of semigroups of bounded linear operators in a general Banach

This paper is concerned with the behavior of semigroups of nonlinear contractions on closed convex subsets of a Hilbert space H. Recently, many results, known for semigroups of linear operators, were extended to semigroups of nonlinear contractions. The first results in this direction by Neuberger [25] and oharu [26] dealt mainly with the representation of such semigroups by means of exponential formulas. Extension of these results and other results of similar nature were obtained by several authors, see e.g. [7], [9], [18], [20], [29] and [34]. The central result in the theory of semigroups of linear operators is the characterization, by the Hille-Yosida theorem, of the generators of semigroups of bounded linear operators in a general Banach space (see e.g. [ll], [35]). S ffi u cient conditions for dissipative operators, or rather dissipative sets, to generate semigroups of contractions, in some class of Banach spaces were obtained by KGmura [16], Kato [12], [13] and Browder [2], [3]. However, a complete characterization, which generalizes the Hille-Yosida theorem, is known only in Hilbert space. These results were obtained independently by Dorroh [IO] for the case of semigroups defined on the whole space and by Crandall and Pazy [7] in the more general case of semigroups defined on a closed convex subset of a Hilbert space. In a Hilbert space H there exists a one-to-one correspondence between