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Bulletin of the American Mathematical Society

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Book Review

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Book Information:

Author: Ioana Cioranescu
Title: Geometry of Banach spaces, duality mappings and nonlinear problems
Additional book information: Kluwer Academic Publishers, Dordrecht, 1990, 260 pp., US$99.00. ISBN 0-7923-0910-3.

References [Enhancements On Off] (What's this?)

  • [1] Ya. I. Al'ber and A. I. Notik, Geometric properties of Banach spaces and approximate methods for solving nonlinear operator equations, Soviet Math. Dokl. 29 (1984), 611-615.
  • [2] E. Asplund, Positivity of duality mappings, Bull. Amer. Math. Soc. 73 (1967), 200-203. MR 0206663 (34:6481)
  • [3] V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Nordhoff Leyden, 1976. MR 0390843 (52:11666)
  • [4] A. Beurling and A. E. Livingston, A theorem on duality mappings in Banach spaces, Ark. Mat. 4 (1962), 405-411. MR 0145320 (26:2851)
  • [5] F. E. Browder, Multivalued monotone nonlinear mappings and duality mappings in Banach spaces, Trans. Amer. Math. Soc. 118 (1965), 338-351. MR 0180884 (31:5114)
  • [6] -, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., vol. XVIII, part 2, Amer. Math. Soc., Providence, RI, 1976. MR 0405188 (53:8982)
  • [7] I. Cioranescu, Aplicatia de dualitate in analiza functionala neliniara, Editura Academiei, Bucuresti, 1974. MR 0383157 (52:4038)
  • [8] J. Dye, M. A. Khamsi, and S. Reich, Random products of contractions in Banach spaces, Trans. Amer. Math. Soc. 325 (1991), 87-99. MR 989572 (91h:47003)
  • [9] J. M. Dye and S. Reich, Unrestricted iterations of nonexpansive mappings in Banach spaces, Center for Applied Mathematical Sciences Report #91-14, Nonlinear Analysis (to appear). MR 1192277 (94b:47070)
  • [10] K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry and nonexpansive mappings, Marcel Dekker, New York and Basel, 1984. MR 744194 (86d:58012)
  • [11] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520. MR 0226230 (37:1820)
  • [12] V. L. Klee, Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10-43. MR 0054850 (14:989d)
  • [13] E. R. Lorch, A curvature study of convex bodies in Banach spaces, Annali Mat. Pura Appl. 34 (1953), 105-112. MR 0052679 (14:657b)
  • [14] G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29-43. MR 0133024 (24:A2860)
  • [15] G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679-698. MR 0132403 (24:A2248)
  • [16] O. Nevanlinna and S. Reich, Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J. Math. 32 (1979), 44-58. MR 531600 (80e:47057)
  • [17] A. T. Plant and S. Reich, The asymptotics of nonexpansive iterations, J. Funct. Anal. 54 (1983), 308-319. MR 724526 (85a:47055)
  • [18] E. I. Poffald and S. Reich, An incomplete Cauchy problem, J. Math. Anal. Appl. 113 (1986), 514-543. MR 826651 (87i:34081)
  • [19] C. R. DePrima and W. V. Petryshyn, Remarks on strict monotonicity and surjectivity properties of duality mappings defined on real normed linear spaces, Math. Z. 123 (1971), 49-55. MR 0308865 (46:7977)
  • [20] S. Reich, Product formulas, nonlinear semigroups and accretive operators, J. Functional Analysis 36 (1980), 147-168. MR 569251 (81k:47076)
  • [21] S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Analysis 15 (1990), 537-558. MR 1072312 (91k:47135)
  • [22] -, An existence theorem for a difference inclusion in general Banach spaces, J. Math. Anal. Appl. 160 (1991), 406-412. MR 1126125 (93a:47076)
  • [23] J. R. L. Webb, On a property of duality mappings and the A-properness of accretive operators, Bull. London Math. Soc. 13 (1981), 235-238. MR 614661 (82f:47065)
  • [24] Z.-B. Xu and G. F. Roach, An alternating procedure for operators on uniformly convex and uniformly smooth Banach spaces, Proc. Amer. Math. Soc. 111 (1991), 1067-1074. MR 1049854 (92a:47026)
  • [25] -, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl. 157 (1991), 189-210. MR 1109451 (92i:46023)

Review Information:

Reviewer: Simeon Reich
Journal: Bull. Amer. Math. Soc. 26 (1992), 367-370
DOI: https://doi.org/10.1090/S0273-0979-1992-00287-2
American Mathematical Society