## Resolvents and selections of accretive mappings in Banach spaces.(English)Zbl 1041.47505

If $$A$$ is a maximal accretive mapping in a Banach space $$X$$ then, under certain additional assumptions, $$\lim_{\lambda\to\infty} \lambda^{-1} (I+\lambda A)^{-1} u=-a^0$$, for each $$u\in D(A)$$, where $$a^0$$ is the element of minimum norm in $$\overline{R(A)}$$. This is a generalization of a result proved in 1976 by the reviewer in the case in which $$X$$ is a Hilbert space [G. Moroşanu, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 61(1976), 565-570 (1977; Zbl 0403.47024)]. The next result of the paper is concerned with almost main selections of maximal accretive mappings and the next and final result is related to approximation of resolvents of accretive mappings.

### MSC:

 47H06 Nonlinear accretive operators, dissipative operators, etc. 49K27 Optimality conditions for problems in abstract spaces

### Keywords:

maximal accretive mapping; approximation of resolvents

Zbl 0403.47024
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