Skip to main content
SpringerLink
Log in

F

  • Chapter
Encyclopaedia of Mathematics

Part of the book series: Encyclopaedia of Mathematics ((ENMA))

  • 1071 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birkhoff, G., and Pierce, R.S.: ‘Lattice-ordered rings’, An. Acad. Brasil. Ci. 28 (1956), 41–69.

    MathSciNet  Google Scholar 

  2. Zaanen, A.C.: Riesz spaces, Vol. II, North-Holland, 1983.

    Google Scholar 

  3. Dao Trong Thi, and Fomenko, A.T.: Minimal surfaces, stratified multivarifolds and the Plateau problem, Amer. Math. Soc., 1991.

    Google Scholar 

  4. Federer, H., and Fleming, W.H.: ‘Normal and integral currents’, Ann. of Math. 72, no. 3 (1960), 458–520.

    Article  MathSciNet  MATH  Google Scholar 

  5. Fomenko, A.T.: Variational principles in topology: multidimensional minimal surface theory, Kluwer Acad. Publ., 1990.

    MATH  Google Scholar 

  6. Barratt, M.G.: ‘Track groups I, II’, Proc. London Math. Soc. 5 (1955), 71–106;

    Article  MathSciNet  MATH  Google Scholar 

  7. Barratt, M.G.: ‘Track groups I, II’, Proc. London Math. Soc. 5 (1955), 285–329.

    Article  MathSciNet  MATH  Google Scholar 

  8. Brown, R.: ‘On Künneth suspensions’, Proc. Cambridge. Philos. Soc. 60 (1964), 713–720.

    Article  MathSciNet  MATH  Google Scholar 

  9. Federer, H.: ‘A study of function spaces by spectral sequences’, Trans. Amer. Math. Soc. 82 (1956), 340–361.

    Article  MathSciNet  MATH  Google Scholar 

  10. Møller, J.M.: ‘On equivariant function spaces’, Pacific J. Math. 142 (1990), 103–119.

    MathSciNet  Google Scholar 

  11. Bassily, N.L.: ‘Approximation theory’: Proc. Conf. Kecksemet, Hungary, 1990, Vol. 58 of Colloq. Math. Soc. Janos Boljai, 1991, pp. 85–96.

    Google Scholar 

  12. Bassily, N.L.: ‘Probability theory and applications. Essays in memory of J. Mogyorodi’, Math. Appl. 80 (1992), 33–45.

    MathSciNet  Google Scholar 

  13. Fefferman, C.: ‘Characterisation of bounded mean oscillation’, Amer. Math. Soc. 77 (1971), 587–588.

    Article  MathSciNet  MATH  Google Scholar 

  14. Garsia, A.M.: Martingale inequalities. Seminar notes on recent progress, Mathematics Lecture Notes. Benjamin, 1973.

    MATH  Google Scholar 

  15. Ishak, S., and Mogyorodi, J.: ‘On the generalization of the Fefferman-Garsia inequality’: Proc. 3rd IFIP-WG17/1 Working Conf., Vol. 36 of Lecture Notes in Control and Information Sciences, Springer, 1981, pp. 85–97.

    Google Scholar 

  16. Ishak, S., and Mogyorodi, J.: ‘On the ‘PΦ-spaces and the generalization of Herz’s and Fefferman inequalities I’, Studia Math. Hungarica 17 (1982), 229–234.

    MathSciNet  MATH  Google Scholar 

  17. Ishak, S., and Mogyorodi, J.: ‘On the PΦ-spaces and the generalization of Herz’s and Fefferman inequalities II’, Studia Math. Hungarica 18 (1983), 205–210.

    MathSciNet  MATH  Google Scholar 

  18. Ishak, S., and Mogyorodi, J.: ‘On the PΦ-spaces and the generalization of Herz’s and Fefferman inequalities III’, Studia Math. Hungarica 18 (1983), 211–219.

    MathSciNet  MATH  Google Scholar 

  19. Boas, R. P.: Entire functions, Acad. Press, 1954.

    MATH  Google Scholar 

  20. Fejer, L.: ‘Über trigonometrische Polynome’, J. Reine Angew. Math. 146 (1916), 53–82.

    Google Scholar 

  21. Helson, H., and Lowdenslager, D.: ‘Prediction theory and Fourier series in several variables I’, Acta Math. 99 (1958), 165–202.

    Article  MathSciNet  MATH  Google Scholar 

  22. Helson, H., and Lowdenslager, D.: ‘Prediction theory and Fourier series in several variables II’, Acta Math. 106 (1961), 175–213.

    Article  MathSciNet  MATH  Google Scholar 

  23. Riesz, F., and Sz.-Nagy, B.: Functional analysis, F. Ungar, 1955.

    Google Scholar 

  24. Rosenblum, M., and Rovnyak, J.: Hardy classes and operator theory, Dover, reprint, 1997.

    MATH  Google Scholar 

  25. Rozanov, Yu. A.: ‘Spectral theory of n-dimensional stationary stochastic processes with discrete time’, Selected Transl. in Math. Statistics and Probab. 1 (1961), 253–306.

    MathSciNet  MATH  Google Scholar 

  26. Rozanov, Yu. A.: ‘Spectral theory of n-dimensional stationary stochastic processes with discrete time’ (Uspekhi Mat. Nauk 13, no. 2 (80) (1958), 93–142.)

    MathSciNet  MATH  Google Scholar 

  27. Szego, G.: Orthogonal polynomials, fourth ed., Vol. 23 of Colloq. Publ., Amer. Math. Soc., 1975.

    Google Scholar 

  28. Wiener, N., and Masani, P.: ‘The prediction theory of multivariate stochastic processes F, Acta Math. 98 (1957), 111–150.

    Article  MathSciNet  MATH  Google Scholar 

  29. Wiener, N., and Masani, P.: ‘The prediction theory of multivariate stochastic processes IF, Acta Math. 99 (1958), 93–137.

    Article  MathSciNet  Google Scholar 

  30. Denis, L.: ‘Le théorème de Fermat-Goss’, Trans. Amer. Math. Soc. 343 (1994), 713–726.

    Article  MathSciNet  MATH  Google Scholar 

  31. Poorten, A.J. Van Der: Notes on Fermat’s last theorem, Wiley, 1996.

    MATH  Google Scholar 

  32. Wiles, A.: ‘Modular elliptic curves and Fermat’s last theorem’, Ann. of Math. 141 (1995), 443–551.

    Article  MathSciNet  MATH  Google Scholar 

  33. Bell, E.T.: The last theorem, Math. Assoc. America, 1990.

    Google Scholar 

  34. Edwards, H.M.: Fermat’s last theorem — A genetic introduction to algebraic number theory, Springer, 1977.

    MATH  Google Scholar 

  35. Ribenboim, P.: 13 lectures on Fermat’s last theorem, Springer, 1979.

    Book  MATH  Google Scholar 

  36. Poorten, A. Van Der: Notes on Fermat’s last theorem, Wiley-Interscience, 1996.

    MATH  Google Scholar 

  37. Wiles, A.: ‘Modular elliptic curves and Fermat’s last theorem’, Ann. of Math. 141 (1995), 443–551.

    Article  MathSciNet  MATH  Google Scholar 

  38. Ahlswede, R., and Daykin, D.E.: ‘An inequality for the weights of two families, their unions and intersections’, Z. Wahrsch. verw. Gebiete 43 (1978), 183–185.

    Article  MathSciNet  MATH  Google Scholar 

  39. Fishburn, P.C.: ‘A correlational inequality for linear extensions of a poset’, Order 1 (1984), 127–137.

    Article  MathSciNet  MATH  Google Scholar 

  40. Shepp, L.A.: ‘The XYZ conjecture and the FKG inequality’, Ann. of Probab. 10 (1982), 824–827.

    Article  MathSciNet  MATH  Google Scholar 

  41. Fitzsimons, P.J., Fristedt, H., and Shepp, L.R.: ‘The set of real numbers left uncovered by random covering intervals’, Z. Wahrscheinlichkeitsth. verw. Gebiete 70 (1985), 175–189.

    Article  Google Scholar 

  42. Mandelbrot, B.B.: ‘Renewal sets and random cutouts’, Z. Wahrscheinlichkeitsth. verw. Gebiete 22 (1972), 145–157.

    Article  MathSciNet  MATH  Google Scholar 

  43. Shepp, L.A.: ‘Covering the line by random intervals’, Z. Wahrscheinlichkeitsth. verw. Gebiete 23 (1972), 163–170.

    Article  MathSciNet  MATH  Google Scholar 

  44. Abian, S., and Brown, A.B.: ‘A theorem on partially ordered sets with applications to fixed point theorems’, Canadian J. Math. 13 (1961), 78–82.

    Article  MathSciNet  MATH  Google Scholar 

  45. Baclawski, K., and Björner, A.: ‘Fixed points in partially ordered sets’, Adv. Math. 31 (1979), 263–287.

    Article  MATH  Google Scholar 

  46. Davis, A.C.: ‘A characterization of complete lattices’, Pacific J. Math. 5 (1955), 311–319.

    MathSciNet  MATH  Google Scholar 

  47. Dreesen, B., Poguntke, W., and Winkler, P.: ‘Comparability invariance of the fixed point property’, Order 2 (1985), 269–274.

    MathSciNet  MATH  Google Scholar 

  48. Duffus, D., and Goddard, T.: ‘The complexity of the fixed point property’, Order 13 (1996), 209–218.

    Article  MathSciNet  MATH  Google Scholar 

  49. Fofanova, T., and Rutkowski, A.: ‘The fixed point property in ordered sets of width two’, Order 4 (1987), 101–106.

    Article  MathSciNet  MATH  Google Scholar 

  50. Heikkilä, S., and Lakhshmikantham, V.: Monotone iterative techniques for discontinuous nonlinear differential equations, M. Dekker, 1994.

    MATH  Google Scholar 

  51. Höft, H., and Höft, M.: ‘Fixed point free components in lexicographic sums with the fixed point property’, Demonstratio Math. XXIV (1991), 294–304.

    Google Scholar 

  52. Li, B., and Milner, E.C.: ‘From finite posets to chain complete posets having no infinite antichain’, Order 12 (1995), 159–171.

    Article  MathSciNet  MATH  Google Scholar 

  53. Pelczar, A.: ‘On the invariant points of a transformation’, Ann. Polonici Math. XI (1961), 199–202.

    MathSciNet  Google Scholar 

  54. Rival, I.: ‘A fixed point theorem for finite partially ordered sets’, J. Combin. Th. A 21 (1976), 309–318.

    Article  MathSciNet  MATH  Google Scholar 

  55. Roddy, M.: ‘Fixed points and products’, Order 11 (1994), 11–14.

    Article  MathSciNet  MATH  Google Scholar 

  56. Schröder, B.: ‘Algorithms vs. the fixed point property’, in I. Rival (ed.): Proc. 1996 ORDAL conference, 1996, To appear in: Theoret. Comput. Sci.

    Google Scholar 

  57. Tarski, A.: ‘A lattice-theoretical fixpoint theorem and its applications’, Pacific J. Math. 5 (1955), 285–309.

    MathSciNet  MATH  Google Scholar 

  58. Xia, W.: ‘Fixed point property and formal concept analysis’, Order 9 (1992), 255–264.

    Article  MathSciNet  MATH  Google Scholar 

  59. Bollobás, B.: Combinatorics, Cambridge Univ. Press, 1986.

    MATH  Google Scholar 

  60. Fishburn, P.C.: ‘Correlation in partially ordered sets’, Discrete Appl. Math. 39 (1992), 173–191.

    Article  MathSciNet  MATH  Google Scholar 

  61. Fortuin, C.M., Kasteleyn, P.N., and Ginibre, J.: ‘Correlation inequalities for some partially ordered sets’, Comm. Math. Phys. 22 (1971), 89–103.

    Article  MathSciNet  MATH  Google Scholar 

  62. Graham, R.L.: ‘Linear extensions of partial orders and the FKG inequality’, in I. Rival (ed.): Ordered sets, Reidel, 1982, pp. 213–236.

    Google Scholar 

  63. Graham, R.L.: ‘Applications of the FKG inequality and its relatives’: Proc. 12th Internat. Symp. Math. Programming, Springer, 1983, pp. 115–131.

    Google Scholar 

  64. Holley, R.: ‘Remarks on the FKG inequalities’, Comm. Math. Phys. 36 (1974), 227–231.

    Article  MathSciNet  Google Scholar 

  65. Joag-Dev, K., Shepp, L.A., and Vitale, R.A.: ‘Remarks and open problems in the area of the FKG inequality’: Inequalities Stat. Probab., Vol. 5 of IMS Lecture Notes, 1984, pp. 121–126.

    MathSciNet  Google Scholar 

  66. Shepp, L.A.: ‘The XYZ conjecture and the FKG inequality’, Ann. of Probab. 10 (1982), 824–827.

    Article  MathSciNet  MATH  Google Scholar 

  67. Winkler, P. M.: ‘Correlation and order’, Contemp. Math. 57 (1986), 151–174.

    Article  Google Scholar 

  68. Hastad, J.: ‘Dual vectors and lower bounds for the nearest lattice point problem’, Combinatorica 8 (1988), 75–81.

    Article  MathSciNet  MATH  Google Scholar 

  69. Lagarias, J., Lenstra, H.W., and Schnorr, C.P.: ‘Korkine-Zolotarev bases and successive minima of a lattice and its reciprocal lattice’, Combinatorica 10 (1990), 333–348.

    Article  MathSciNet  MATH  Google Scholar 

  70. Bader, L., and Lunardon, G.: ‘On the flocks of Q+(3,q)’, Geom. Dedicata 29 (1989), 177–183.

    Article  MathSciNet  MATH  Google Scholar 

  71. Biliotti, M., and Jclinson, N.L.: ‘Variations on a theme of Dembowski’: Proc. AMS Conf. Iowa City, 1996.

    Google Scholar 

  72. Biliotti, M., and Johnson, N.L.: ‘Bilinear flocks of quadratic cones’, J. Geom. (to appear).

    Google Scholar 

  73. Dembowski, P.: Finite geometries, Springer, 1967.

    Google Scholar 

  74. Jha, V., and Johnson, N.L.: ‘Structure theory for point-Baer and line-Baer collineation groups in affine planes’: Proc. Amer. Math. Soc. Conf. Iowa City, 1996.

    Google Scholar 

  75. Johnson, N.L.: ‘Flocks of hyperbolic quadrics and translation planes admitting affine homologies’, J. Geom. 34 (1989), 50–73.

    Article  MathSciNet  MATH  Google Scholar 

  76. Johnson, N.L.: ‘Flocks of infinite hyperbolic quadrics’, J. Algebraic Combinatorics 1 (1997), 27–51.

    Google Scholar 

  77. Payne, S.E., and Thas, J.A.: ‘Conical flocks, partial flocks, derivation and generalized quadrangles’, Geom. Ded. 38 (1991), 229–243.

    Article  MathSciNet  MATH  Google Scholar 

  78. Thas, J.A.: ‘Flocks of egglike inversive planes’, in A. Barlotti (ed.): Finite Geometric Structures and their Applications, 1973, pp. 189–191.

    Google Scholar 

  79. Thas, J.A.: ‘Generalized quadrangles and flocks of cones’, Europ. J. Comb. 8 (1987), 441–452.

    MathSciNet  MATH  Google Scholar 

  80. Thas, J.A.: ‘Flocks, maximal exterior sets and inversive planes’, Contemp. Math. 111 (1990), 187–218.

    Article  MathSciNet  Google Scholar 

  81. Baldwin, J.T.: Fundamentals of stability theory, Springer, 1987.

    Google Scholar 

  82. Harnik, V., and Harrington, L.: ‘Fundamentals of forking’, Ann. Pure and Applied Logic 26 (1984), 245–286.

    Article  MathSciNet  MATH  Google Scholar 

  83. Keisler, H.J.: ‘Measures and forking’, Ann. Pure and Applied Logic 34 (1987), 119–169.

    Article  MathSciNet  MATH  Google Scholar 

  84. Lascar, D., and Poizat, B.: ‘An introduction to forking’, J. Symbolic Logic 44 (1979), 330–350.

    Article  MathSciNet  MATH  Google Scholar 

  85. Makkai, M.: ‘A survey of basic stability theory’, Israel J. Math. 49 (1984), 181–238.

    Article  MathSciNet  MATH  Google Scholar 

  86. Pillay, A.: Introduction to stability theory, Oxford Univ. Press, 1983.

    Google Scholar 

  87. Pillay, A.: ‘The geometry of forking and groups of finite Morley rank’, J. Symbolic Logic 60 (1995), 1251–1259.

    Article  MathSciNet  MATH  Google Scholar 

  88. Prest, M.: Model theory and modules, Cambridge Univ. Press, 1988.

    Book  MATH  Google Scholar 

  89. Shelah, S.: Classification theory and the number of non-isomorphic models, revised ed., North-Holland, 1990.

    MATH  Google Scholar 

  90. Ehrenfeucht, A.: ‘An application of games to the completeness problem for formalised theories’, Fundam. Math. 49 (1956), 129–141.

    MathSciNet  Google Scholar 

  91. Fraïssé, R.: ‘Sur quelques classifications des relations basés sur des isomorphismes restraintes’, Publ. Sci. Univ. Alger. Ser. A 2 (1955), 11–60.

    Google Scholar 

  92. Fraïssé, R.: ‘Sur quelques classifications des relations basés sur des isomorphismes restraintes’, Publ. Sci. Univ. Alger. Ser. A 2 (1955), 273–295.

    MathSciNet  Google Scholar 

  93. Hintikka, J.: ‘Distributive normal forms in first order logic’, in J.N. Crossley and M.A.E. Dummet (eds.): Formal Systems and Recursive Functions, North-Holland, 1965, pp. 48–91.

    Chapter  Google Scholar 

  94. Keisler, H.J.: ‘Ultraproducts and elementary classes’, Indagationes Mathematicae 23 (1961), 277–295.

    MathSciNet  Google Scholar 

  95. Kochen, S.: ‘Ultraproducts in the theory of models’, Ann. of Math. 74 (1961), 231–261.

    Article  MathSciNet  Google Scholar 

  96. Mostowski, A.: Thirty years of foundational studies, Barnes and Noble, 1966.

    Google Scholar 

  97. Scott, D.: ‘Logic with denumerably long formulas and finite strings of quantifiers’, in J.W. Addison, L. Henkin, and A. Tarski (eds.): The Theory of Models, North-Holland, 1966, pp. 329–341.

    Google Scholar 

  98. Weaver, G., and Welaish, J.: ‘Back and forth arguments in modal logic’, J. Symb. Logic 51 (1987), 969–980.

    Article  MathSciNet  Google Scholar 

  99. Beckenstein, E., Narici, L., and Suffel, C.: Topological algebras, Amsterdam, 1977.

    MATH  Google Scholar 

  100. Husain, T.: Multiplicative functional on topological algebras, London, 1983.

    Google Scholar 

  101. Mallios, A.: Topological algebras. Selected topics, Amsterdam, 1986.

    MATH  Google Scholar 

  102. Michael, E.: Locally multiplicatively-convex topological algebras, Vol. 11 of Memoirs, Amer. Math. Soc., 1952.

    Google Scholar 

  103. Waelbroeck, L.: Topological vector spaces and algebras, Vol. 230 of Lecture Notes in Mathematics, Springer, 1971.

    Google Scholar 

  104. Zelazko, W.: ‘Metric generalizations of Banach algebras’, Dissert. Math. 47 (1965).

    Google Scholar 

  105. Zelazko, W.: Selected topics in topological algebras, Vol. 31 of Lecture Notes, Aarhus Univ., 1971.

    Google Scholar 

  106. Banach, S.: Théorie des operations lineaires, Warszawa, 1932.

    Google Scholar 

  107. Bourbaki, N.: Espaces vectorielles topologiques, Paris, 1981.

    Google Scholar 

  108. Dunford, N., and Schwartz, J.T.: Linear operators, Vol. I. General theory, Wiley, reprint, 1988.

    Google Scholar 

  109. Grothendieck, A.: Topological vector spaces, New York, 1973.

    MATH  Google Scholar 

  110. Jarchow, H.: Locally convex spaces, Teubner, 1981.

    Book  MATH  Google Scholar 

  111. Köthe, G.: Topological vector spaces, Vol. I–II, New York, 1969–1979.

    Google Scholar 

  112. Rolewicz, S.: Metric linear spaces, PWN & Reidel, 1972.

    MATH  Google Scholar 

  113. Schaefer, H.H.: Topological vector spaces, Springer, 1971.

    Google Scholar 

  114. Waelbroeck, L.: Topological vector spaces and algebras, Vol. 230 of Lecture Notes in Mathematics, Springer, 1971.

    Google Scholar 

  115. Wilansky, A.: Modern methods in topological vector spaces, New York, 1978.

    MATH  Google Scholar 

  116. Bourbaki, N.: Groupes et algèbres de Lie, Vol. 2: Algebres de Lie libres, Hermann, 1972.

    MATH  Google Scholar 

  117. Reutenauer, C.: Free Lie algebras, Oxford Univ. Press, 1993.

    MATH  Google Scholar 

  118. Serre, J.-P.: Lie algebras and Lie groups, Benjamin, 1965.

    MATH  Google Scholar 

  119. Kannan, R.: ‘Lattice translates of a polytope and the Frobenius problem’, Combinatorica 12 (1992), 161–172.

    Article  MathSciNet  MATH  Google Scholar 

  120. Lovász, L.: ‘Geometry of numbers and integer programming’, in M. Iri and K. Tanabe (eds.): Mathematical Programming, Kluwer Acad. Publ., 1989, pp. 177–202.

    Google Scholar 

  121. Frucht, R.: ‘Herteilung von Graphen mit vorgegebenen Abstrakten Gruppen’, Compositio Math. 6 (1938), 239–250.

    MathSciNet  MATH  Google Scholar 

  122. Frucht, R.: ‘Graphs of degree three with a given abstract group’, Canad. J. Math. 1 (1949), 365–378.

    Article  MathSciNet  MATH  Google Scholar 

  123. König, D.: Theorie der Endlichen und Unendlichen Graphen, Leipzig, 1936.

    Google Scholar 

  124. Krishnamoorthy, V., and Parthasarathy, K.R.: ‘F-sets in graphs’, J. Combin. Theory B 24 (1978), 53–60.

    Article  MathSciNet  Google Scholar 

  125. Lovász, L.: Combinatorial problems and exercises, North-Holland, 1979.

    MATH  Google Scholar 

  126. Sabidussi, G.: ‘Graphs with given groups and given graph-theoretical properties’, Canad. J. Math. 9 (1957), 515–525.

    Article  MathSciNet  MATH  Google Scholar 

  127. Watkins, M.E.: ‘On the action of non-abelian groups on graphs’, J. Combin. Theory 11 (1971), 95–104.

    Article  MathSciNet  MATH  Google Scholar 

  128. Ando, T.: ‘Some operator inequalities’, Math. Ann. 279 (1987), 157–159.

    Article  MathSciNet  MATH  Google Scholar 

  129. Ando, T., and Hiai, F.: ‘Log majorization and complementary Golden-Thompson type inequality’, Linear Alg. & Its Appl. 197/198 (1994), 113–131.

    Article  MathSciNet  Google Scholar 

  130. Fujii, M.: ‘Furuta’s inequality and its mean theoretic approach’, J. Operator Th. 23 (1990), 67–72.

    MATH  Google Scholar 

  131. Fujii, M., and Kamei, E.: ‘Mean theoretic approach to the grand Furuta inequality’, Proc. Amer. Math. Soc. 124 (1996), 2751–2756.

    Article  MathSciNet  MATH  Google Scholar 

  132. Furuta, T.: ‘A ≥ B ≥ 0 assures (BrApBr)1/q ≥ B(p+2r)/q for r ≥ 0, p ≥ 0, q ≥ 1with (1 + 2r)q ≥ p + 2r’, Proc. Amer. Math. Soc. 101 (1987), 85–88.

    MathSciNet  MATH  Google Scholar 

  133. Furuta, T.: ‘Elementary proof of an order preserving inequality’, Proc. Japan Acad. 65 (1989), 126.

    Article  MathSciNet  MATH  Google Scholar 

  134. Furuta, T.: ‘Extension of the Furuta inequality and Ando-Hiai log-majorization’, Linear Alg. & Its Appl. 219 (1995), 139–155.

    Article  MathSciNet  MATH  Google Scholar 

  135. Kamei, E.: ‘A satellite to Furuta’s inequality’, Math. Japon. 33 (1988), 883–886.

    MathSciNet  MATH  Google Scholar 

  136. Kubo, F., and Ando, T.: ‘Means of positive linear operators’, Math. Ann. 246 (1980), 205–224.

    Article  MathSciNet  MATH  Google Scholar 

  137. Tanahashi, K.: ‘Best possibility of the Furuta inequality’, Proc. Amer. Math. Soc. 124 (1996), 141–146.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. M. Hazewinkel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. Hazewinkel

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Kluwer Academic Publishers

About this chapter

Cite this chapter

Hazewinkel, M. (1997). F. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1288-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-1288-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4896-7

  • Online ISBN: 978-94-015-1288-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation