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Book Review
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Book Information
Author(s):
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:
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- Ya. I. Al\cprime ber and A. I. Notik, Geometric properties of Banach spaces and approximate methods for solving nonlinear operator equations, Soviet Math. Dokl. \textbf{29} (1984), 611--615.
- [2]
- E. Asplund, Positivity of duality mappings, Bull. Amer. Math. Soc. \textbf{73} (1967), 200--203.
- [3]
- V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Nordhoff, Leyden, 1976.
- [4]
- A. Beurling and A. E. Livingston, A theorem on duality mappings in Banach spaces, Ark. Mat. \textbf{4} (1962), 405--411.
- [5]
- F. E. Browder, Multivalued monotone nonlinear mappings and duality mappings in Banach spaces, Trans. Amer. Math. Soc. \textbf{118} (1965), 338--351.
- [6]
- F. E. Browder, \emph{Nonlinear operators and nonlinear equations of evolution in Banach spaces} vol.~XVIII, part 2, Amer. Math. Soc., Providence, RI, 1976.
- [7]
- I. Cioranescu, Aplicatia de dualitate in analiza functionala neliniara, Editura Academiei, Bucuresti, 1974.
- [8]
- J. Dye, M. A. Khamsi, and S. Reich, Random products of contractions in Banach spaces, Trans. Amer. Math. Soc. \textbf{325} (1991), 87--99.
- [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.
- [10]
- K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry and nonexpansive mappings, Marcel Dekker, New York and Basel, 1984.
- [11]
- T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan \textbf{19} (1967), 508--520.
- [12]
- V. L. Klee, Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. \textbf{74} (1953), 10--43.
- [13]
- E. R. Lorch, A curvature study of convex bodies in Banach spaces, Annali Mat. Pura Appl. \textbf{34} (1953), 105--112.
- [14]
- G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. \textbf{100} (1961), 29--43.
- [15]
- G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. \textbf{11} (1961), 679--698.
- [16]
- O. Nevanlinna and S. Reich, Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J. Math. \textbf{32} (1979), 44--58.
- [17]
- A. T. Plant and S. Reich, The asymptotics of nonexpansive iterations, J. Funct. Anal. \textbf{54} (1983), 308--319.
- [18]
- E. I. Poffald and S. Reich, An incomplete Cauchy problem, J. Math. Anal. Appl. \textbf{113} (1986), 514--543.
- [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. \textbf{123} (1971), 49--55.
- [20]
- S. Reich, Product formulas, nonlinear semigroups and accretive operators, J. Functional Analysis \textbf{36} (1980), 147--168.
- [21]
- S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Analysis \textbf{15} (1990), 537--558.
- [22]
- S. Reich and I. Shafrir, An existence theorem for a difference inclusion in general Banach spaces, J. Math. Anal. Appl. \textbf{160} (1991), 406--412.
- [23]
- J. R. L. Webb, On a property of duality mappings and the $A$-properness of accretive operators, Bull. London Math. Soc. \textbf{13} (1981), 235--238.
- [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. \textbf{111} (1991), 1067--1074.
- [25]
- Z.-B. Xu and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl. \textbf{157} (1991), 189--210.
Additional Information:
Reviewer(s):
Simeon
Reich
Review Information:
Journal:
Bull. Amer. Math. Soc.
26
(1992),
367-370.
DOI:
10.1090/S0273-0979-1992-00287-2
PII:
S 0273-0979(1992)00287-2
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