Curriculum Vitae and Publications
Ronald E. Bruck
Date and place of birth:
June 1, 1943
Wichita Falls, Texas
Education:
S.B. University of Chicago June 1964
S.M. University of Chicago June 1965
Ph.D. University of Chicago June 1969
Dissertation:
"Approximating fixed points and fixed point sets of nonexpansive mappings in Banach spaces"
Felix Browder, Thesis Advisor
Employment:
1969-1974 Assistant Professor of Mathematics
University of Southern California
1975-1982 Associate Professor of Mathematics
University of Southern California
1977 Visiting Associate Professor of Mathematics
University of Chicago
1982- Professor of Mathematics
University of Southern California
1983-84 Visiting Professor of Mathematics
University of Iowa
1978-83 Graduate Vice Chairman
Department of Mathematics
University of Southern California
1985-90 Chairman
Department of Mathematics
University of Southern California
May-Jun Professeur Associé
1987 Université Lyon I
Jan-Jun Visiting Member,
1991 Laboratoire d'Analyse Numerique, U. Paris VI
1993– Director, Mathematics Computing Labs
University of Southern California
July 1996 Professeur Associé
Université Lyon I
July 2006 Professeur Associé
Sorbonne (Université Paris I)
Research Support
1972 NSF Grant GP-30221
Structure of fixed-point sets of nonexpansive and pseudocontractive mappings in Banach spaces
1973 NSF Grant GP-38516
The structure of nonexpansive retracts of Banach spaces and the fixed-point sets of nonexpansive and pseudocontractive mappings
1975 NSF Grant 75-09375
Asymptotic convergence of contraction semigroups in Hilbert space
1976-77 NSF Grant 76-08217
Asymptotic convergence of quasi-contraction semigroups and convergence of related iteration methods
1978-80 NSF Grant 78-02305 (with S. Reich)
Behavior of nonlinear evolution systems in infinite-dimensional Banach spaces
1981-83 NSF Grant 81-02806 (with S. Reich)
Nonlinear evolution equations in infinite-dimensional Banach spaces
Publications
1. Nonexpansive retracts of Banach spaces, Bull. Amer. Math. Soc. 76 (1970), 384-386.
2. Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 251-262.
3. On the iterative solution of the equation y Î x + Tx for a monotone operator T in Hilbert space, Bull. Amer. Math. Soc. 79 (1973), 1258-1261.
4. A characterization of Hilbert space, Proc. Amer. Math. Soc. 43 (1974), 173-175.
5. Nonexpansive projections on subsets of Banach spaces, Pacific J. Math. 47 (1973), 341-355.
6. A strongly convergent iterative solution of 0 Î U(x) for a maximal monotone operator U in Hilbert space, J. Math. Anal. Appl. 48 (1974), 114-126.
7. A common fixed point theorem for a commuting family of nonexpansive mappings, Pacific J. Math. 58 (1974), 59-71.
8. Asymptotic convergence of nonlinear contraction semigroups in Hilbert space, J. Functional Anal. 18 (1975), 15-26.
9. A common fixed point theorem for compact convex semigroups of nonexpansive mappings, Proc. Amer. Math. Soc. 53 (1975), 113-116.
10. An iterative solution of a variational inequality for certain monotone operators in Hilbert space, Bull. Amer. Math. Soc. 81 (1975), 890-892; corrigendum, 82 (1976), 353.
11. On the structure of the fixed-point set of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 61 (1976), 16-18.
12. On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space, J. Math. Anal. Appl. 61 (1977), 159-164.
13. On the strong convergence of an averaging iteration for the solution of operator equations involving monotone operators in Hilbert space, J. Math. Anal. Appl. 64 (1978), 319-327.
14. On the almost-convergence of the iterates of a nonexpansive mapping in Hilbert space and the structure of the weak w-limit set, Israel J. Math. 29 (1978), 1-16.
15. (With J.-B. Baillon and S. Reich) On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, Houston J. Math. 4 (1978), 1-9.
16. (With S. Reich) Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math. 3 (1977), 459-470.
17. A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J. Math. 32 (1979), 107-116.
18. (With G. Passty) Almost convergence of the infinite product of resolvents in Banach spaces, Nonlinear Analysis 3 (1979), 107-116.
19. (With S. Reich) A general convergence principle in nonlinear functional analysis, Nonlinear Analysis 4 (1980), 939-950.
20. Periodic forcing of solutions of a boundary value problem for a second-order differential equation in Hilbert space, J. Math. Anal. Appl. 76 (1980), 939-950.
21. On the weak asymptotic almost-periodicity of bounded solutions of u" Î Au + f for monotone A, J. Diff. Equations 37 (1980), 309-317.
22. On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces, Israel J. Math. 38 (1981), 304-314.
23. (With S. Reich) Accretive operators, Banach limits, and dual ergodic theorems, Bull. Acad. Polon. Sci. Math. Astron. Phys. XXIX (1981), 585-589.
24. (With W. A Kirk and S. Reich) Strong and weak convergence theorems for locally nonexpansive mappings in Banach spaces, Nonlinear Analysis 6 (1982), 151-155.
25. Random products of contractions in metric and Banach spaces, J. Math. Anal. Appl. 88 (1982), 319-332.
26. Asymptotic behavior of nonexpansive mappings, in Contemporary Mathematics, v. 18, Fixed Points and Nonexpansive Mappings, (1983) pp. 1-47.
27. Construction of periodic solutions of periodic contractive evolution systems from bounded solutions, in Proceedings of Symposia in Pure Mathematics, v. 45, Nonlinear Functional Analysis and Applications, (1986), pp. 227–235.
28. Structure of the Approximate Fixed-Point Sets of Nonexpansive Mappings in General Banach Spaces, in Fixed Point Theory and Applications (Marseille, 1989), Pitman Res. Notes Math. Ser. 252 (1991), pp. 91–96.
29. (With K. Goebel) Bizarre Fixed-Point Sets, in Proceedings of the Second International Conference on Fixed Point Theory and Applications, World Scientific Press, London, 1992, pp. 12–26.
30. (With J.-B. Baillon) Optimal rates of asymptotic regularity for averaged nonexpansive mappings, in Proceedings of the Second International Conference on Fixed Point Theory and Applications, World Scientific Press, London, 1992, pp. 27–66.
31. (With J.-B. Baillon) Ergodic theorems and the asymptotic behavior of contraction semigroups, in Proceedings of the Second International Conference on Fixed Point Theory and Applications, World Scientific Press, London, 1992, pp. 13–26.
32. (With T. Kuczumow and S. Reich) Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloquium Mathematicum LXV (1993), 169–179.
33. (With J.-B. Baillon) The rate of asymptotic regularity is O(1/√n), in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, Marcel Dekker, 1996, pp. 51–81.
34. A simple proof that the rate of asymptotic regularity of (I+T)/2 is O(1/√n), in Recent Advances on Metric Fixed Point Theory, Universidad de Sevilla, 1996, Sevilla, pp. 11–18.
35. (With J.-B. Baillon) On the random product of orthogonal projections in Hilbert space, Nonlinear Analysis and Convex Analysis (Niigata 1998), World Sci. Publishing, 199, River Edge, NJ, pp. 126-133.
36. On the random product of orthonal projections in Hilbert space II, in Nonlinear analysis and optimization : a conference in celebration of Alex Ioffe's 70th and Simeon Reich's 60th birthdays, June 18-24, 2008, Haifa, Israel / Arie Leizarowitz ... [et al.], editors. Israel mathematical conference proceedings. Contemporary Mathematics ; 513-514. Conference on Nonlinear Analysis and Optimization (2008 : Haifa, Israel). Providence, R.I. : American Mathematical Society ; Ramat-Gan, Israel : Bar-Ilan University, c2010.
Bruck CV p. XXX