On the Yosida approximation of operators. (English) Zbl 1001.47031
Summary: A generalized Yosida approximation of monotone (and non-monotone) operators in Banach space is introduced. It uses a general potential that is not necessarily the square of the norm. It is therefore advisable to use it in cases where some other more convenient potentials are available, such as in \(L_p\)-spaces. As an illustration, the case of Nemyckij operators is considered.
MSC:
| 47H05 | Monotone operators and generalizations |
| 47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |
| 47A58 | Linear operator approximation theory |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
