On the generation of semigroups of nonlinear contractions

Shinnosuke OHARU

doi:10.2969/jmsj/02240526

Shinnosuke OHARU

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JOURNAL FREE ACCESS

1970 Volume 22 Issue 4 Pages 526-550

DOI https://doi.org/10.2969/jmsj/02240526

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Published: 1970 Received: December 10, 1969 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Brezis and A. Pazy, Semi-groups of nonlinear contractions on convex sets, to appear in J. Func. Anal.
2) M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Func. Anal., 3 (1969), 376-418.
3) M. G. Crandall and A. Pazy, On accretive sets in Banach spaces, J. Func. Anal., 5 (1970), 204-217.
4) J. R. Dorroh, A nonlinear Hille-Yosida-Phillips theorem, J. Func. Anal., 3 (1969), 345-353.
5) J. R. Dorroh, Some classes of semi-groups of nonlinear transformations and their generators, J. Math. Soc. Japan, 20 (1968), 437-455.
6) J. R. Dorroh, Semi-groups of nonlinear transformations, Michigan Math. J., 12 (1965), 317-320.
7) E. Hille and R. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ., 31, 1957.
8) Y. Komura, Nonlinear semigroups in Hilbert space, J. Math. Soc. Japan, 19 (1967), 493-507.
9) Y. Komura, Differentiability of nonlinear semigroups, J. Math. Soc. Japan, 21 (1969), 375-402.
10) T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 503-520.
11) T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symposium Nonlinear Func. Anal. Amer. Math. Soc. (1968) (to appear).
12) I. Miyadera, On the convergence of nonlinear semigroups, Tohoku Math. J., 21 (2) (1969), 221-236.
13) I. Miyadera, On the convergence of nonlinear semigroups, II, J. Math. Soc. Japan, 21 (1969), 403-412.
14) I. Miyadera and S. Oharu, Approximation of semi-groups of nonlinear operators, Tohoku Math. J., 22 (1970), 24-47.
15) S. Oharu, Note on the representation of semi-groups of nonlinear operators, Proc. Japan Acad., 42 (1966), 1149-1154.
16) S. Oharu, Nonlinear semigroups in Banach spaces, to appear.
17) S. Oharu, A note on the generation of nonlinear semigroups in a locally convex space, Proc. Japan Acad., 43 (9) (1967), 847-851.
18) W. V. Petryshyn, Remarks on fixed point theorems and their extensions, Trans. Amer. Math. Soc., 12 (1) (1967), 43-53.
19) J. T. Schwartz, Nonlinear Functional Analysis, (1963-1964), Courant Inst. of Math. Sci., New York Univ.
20) J. Watanabe, Semi-groups of nonlinear operators on closed convex sets, proc. Japan Acad., 45 (4) (1969), 219-223.

Right : [1] H. Brezis and A. Pazy, Semi-groups of nonlinear contractions on convex sets, to appear in J. Func. Anal.
[2] M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Func. Anal., 3 (1969), 376-418.
[3] M. G. Crandall and A. Pazy, On accretive sets in Banach spaces, J. Func. Anal., 5 (1970), 204-217.
[4] J. R. Dorroh, A nonlinear Hille-Yosida-Phillips theorem, J. Func. Anal., 3 (1969), 345-353.
[5] J. R. Dorroh, Some classes of semi-groups of nonlinear transformations and their generators, J. Math. Soc. Japan, 20 (1968), 437-455.
[6] J. R. Dorroh, Semi-groups of nonlinear transformations, Michigan Math. J., 12 (1965), 317-320.
[7] E. Hille and R. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ., 31, 1957.
[8] Y. Komura, Nonlinear semigroups in Hilbert space, J. Math. Soc. Japan, 19 (1967), 493-507.
[9] Y. Komura, Differentiability of nonlinear semigroups, J. Math. Soc. Japan, 21 (1969), 375-402.
[10] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 503-520.
[11] T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symposium Nonlinear Func. Anal. Amer. Math. Soc. (1968) (to appear).
[12] I. Miyadera, On the convergence of nonlinear semigroups, Tôhoku Math. J., 21 (2) (1969), 221-236.
[13] I. Miyadera, On the convergence of nonlinear semigroups, II, J. Math. Soc. Japan, 21 (1969), 403-412.
[14] I. Miyadera and S. Oharu, Approximation of semi-groups of nonlinear operators, Tôhoku Math. J., 22 (1970), 24-47.
[15] S. Oharu, Note on the representation of semi-groups of nonlinear operators, Proc. Japan Acad., 42 (1966), 1149-1154.
[16] S. Oharu, Nonlinear semigroups in Banach spaces, to appear.
[17] S. Oharu, A note on the generation of nonlinear semigroups in a locally convex space, Proc. Japan Acad., 43 (9) (1967), 847-851.
[18] W. V. Petryshyn, Remarks on fixed point theorems and their extensions, Trans. Amer. Math. Soc., 12 (1) (1967), 43-53.
[19] J. T. Schwartz, Nonlinear Functional Analysis, (1963-1964), Courant Inst. of Math. Sci., New York Univ.
[20] J. Watanabe, Semi-groups of nonlinear operators on closed convex sets, Proc. Japan Acad., 45 (4) (1969), 219-223.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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