Bulletin of the American Mathematical Society

MathSciNet review: 1567976
Full text of review: PDF   This review is available free of charge.
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.

[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.

Edgar Asplund, Positivity of duality mappings, Bull. Amer. Math. Soc. 73 (1967), 200–203. MR 206663, DOI 10.1090/S0002-9904-1967-11678-1

Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR 0390843

Arne Beurling and A. E. Livingston, A theorem on duality mappings in Banach spaces, Ark. Mat. 4 (1962), 405–411 (1962). MR 145320, DOI 10.1007/BF02591622

Felix E. Browder, Multi-valued monotone nonlinear mappings and duality mappings in Banach spaces, Trans. Amer. Math. Soc. 118 (1965), 338–351. MR 180884, DOI 10.1090/S0002-9947-1965-0180884-9

Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188

Ioana Ciorănescu, Aplicaţii de dualitate în analiza funcţională neliniară, Editura Academiei Republicii Socialiste România, Bucharest, 1974 (Romanian). With a French summary and table of contents. MR 0383157

J. Dye, M. A. Khamsi, and S. Reich, Random products of contractions in Banach spaces, Trans. Amer. Math. Soc. 325 (1991), no. 1, 87–99. MR 989572, DOI 10.1090/S0002-9947-1991-0989572-5

John M. Dye and Simeon Reich, Unrestricted iterations of nonexpansive mappings in Banach spaces, Nonlinear Anal. 19 (1992), no. 10, 983–992. MR 1192277, DOI 10.1016/0362-546X(92)90109-R

Kazimierz Goebel and Simeon Reich, Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 83, Marcel Dekker, Inc., New York, 1984. MR 744194

Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508–520. MR 226230, DOI 10.2969/jmsj/01940508

Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10–43. MR 54850, DOI 10.1090/S0002-9947-1953-0054850-X

E. R. Lorch, A curvature study of convex bodies in Banach spaces, Ann. Mat. Pura Appl. (4) 34 (1953), 105–112. MR 52679, DOI 10.1007/BF02415327

G. Lumer, Semi-inner-product spaces, Trans. Amer. Math. Soc. 100 (1961), 29–43. MR 133024, DOI 10.1090/S0002-9947-1961-0133024-2

G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961), 679–698. MR 132403

Olavi Nevanlinna and Simeon Reich, Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J. Math. 32 (1979), no. 1, 44–58. MR 531600, DOI 10.1007/BF02761184

Andrew T. Plant and Simeon Reich, The asymptotics of nonexpansive iterations, J. Funct. Anal. 54 (1983), no. 3, 308–319. MR 724526, DOI 10.1016/0022-1236(83)90003-4

Esteban I. Poffald and Simeon Reich, An incomplete Cauchy problem, J. Math. Anal. Appl. 113 (1986), no. 2, 514–543. MR 826651, DOI 10.1016/0022-247X(86)90323-9

Charles 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 308865, DOI 10.1007/BF01113932

Simeon Reich, Product formulas, nonlinear semigroups, and accretive operators, J. Functional Analysis 36 (1980), no. 2, 147–168. MR 569251, DOI 10.1016/0022-1236(80)90097-X

Simeon Reich and Itai Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. 15 (1990), no. 6, 537–558. MR 1072312, DOI 10.1016/0362-546X(90)90058-O

Simeon Reich and Itai Shafrir, An existence theorem for a difference inclusion in general Banach spaces, J. Math. Anal. Appl. 160 (1991), no. 2, 406–412. MR 1126125, DOI 10.1016/0022-247X(91)90313-O

J. R. L. Webb, On a property of duality mappings and the $A$-properness of accretive operators, Bull. London Math. Soc. 13 (1981), no. 3, 235–238. MR 614661, DOI 10.1112/blms/13.3.235

Zong Ben Xu and G. F. Roach, An alternating procedure for operators on uniformly convex and uniformly smooth Banach spaces, Proc. Amer. Math. Soc. 111 (1991), no. 4, 1067–1074. MR 1049854, DOI 10.1090/S0002-9939-1991-1049854-3

Zong Ben Xu and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl. 157 (1991), no. 1, 189–210. MR 1109451, DOI 10.1016/0022-247X(91)90144-O

[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)