Skip to main content

Fixed Point Theory of Multivalued Weighted Maps

  • Chapter

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Abraham and J. Robbin, Transversal mappings and flows, An appendix by Al Kelley (1967), W. A. Benjamin, Inc., New York-Amsterdam.

    Google Scholar 

  2. F. J. Almgren, Applications of multiple-valued functions, Geometric Modeling, SIAM, Philadelphia, PA, 1987, pp. 43–54.

    Google Scholar 

  3. _____, Multi-functions mod v, Geometric Analysis and Computer Graphics (Berkeley, CA, 1988), vol. 17, Math. Sci. Res. Inst. Publ., Springer, New York, 1991, pp. 1–17.

    Google Scholar 

  4. G. Anichini and G. Conti, About the existence of solutions of a boundary value problem for a Carathéodory differential system, Z. Anal. Anwendungen 16 (1997), 621–630.

    MathSciNet  MATH  Google Scholar 

  5. R. Bader, G. Gabor and W. Kryszewski, On the extension of approximations for set-valued maps and the repulsive fixed points., Boll. Un. Mat. Ital. B (7) 10 (1996), 399–416.

    MathSciNet  MATH  Google Scholar 

  6. J. C. Becker, A. Casson and D. H. Gottlieb, The Lefschetz number and fiber preserving maps, Bull. Amer. Math. Soc. 81 (1975), 425–427.

    MathSciNet  MATH  Google Scholar 

  7. J. C. Becker and D. H. Gottlieb, The transfer map and fiber bundles, Topology 14 (1975), 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  8. _____, Vector fields and transfers, Manuscripta Math. 72 (1991), 111–130.

    MathSciNet  MATH  Google Scholar 

  9. J. C. Becker and R. E. Schultz, Fixed-point indices and left invariant framings, Geometric Applications of Homotopy Theory, Proc. Conf. Evanston (Ill., 1977), I, vol. 657, Lecture Notes in Math., Springer, Berlin, 1978, pp. 1–31.

    Google Scholar 

  10. _____, Axioms for bundle transfers and traces, Math. Z. 227 (1998), 583–605.

    Article  MathSciNet  MATH  Google Scholar 

  11. Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis and V. V. Obukhovskiĭ, New results in the theory of multivalued mappings I Topological characteristics and solvability of operator relations, Mathematical Analysis, vol. 25, Itogi Nauki i Tekhniki, pp. 123–197, 200 (Russian); Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform. Moscow, 1987; transl. in J. Soviet Math. 49 (1990), 800–855.

    Google Scholar 

  12. G. E. Bredon, Sheaf Theory, Graduate Texts in Mathematics, vol. 170, Springer-Verlag, New York, 1997.

    Google Scholar 

  13. R. Caccioppoli, Funzioni di variabili complesse. Equazioni funzionali, Opere, vol. II, Edizioni Cremonese, Rome, 1963.

    Google Scholar 

  14. R. Connelly, An extension of Brouwer's fixed-point theorem to nonacyclic, set valued functions, Proc. Amer. Math. Soc. 43 (1974), 214–218.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Conti, P. Nistri and P. Zecca, Systems of set-valued equations in Banach spaces, Delay Differential Equations and Dynamical Systems (Claremont, CA, 1990), Lecture Notes in Math., vol. 1475, Springer, Berlin, 1991, pp. 98–109.

    Google Scholar 

  16. _____, Systems of multivalued equations for solving controllability problems, Pure Math. Appl. Ser. B 2 (1992), 215–225.

    MathSciNet  Google Scholar 

  17. G. Conti and J. Pejsachowicz, Fixed point theorems for multivalued weighted maps, Ann. Mat. Pura Appl. (4) 126 (1981), 319–341.

    MathSciNet  Google Scholar 

  18. L. Dal Soglio, Grado topologico e teoremi di esistenza di punti uniti per trasformazioni plurivalenti di 3-celle., Rend. Sem. Mat. Univ. Padova 25 (1956), 386–405.

    MATH  MathSciNet  Google Scholar 

  19. _____, Grado topologico e teoremi di esistenza di punti uniti per trasformazioni plurivalenti di n-celle, Rend. Sem. Mat. Univ. Padova 27 (1957), 103–121.

    MATH  MathSciNet  Google Scholar 

  20. _____, Sulla nozione di grado e di coefficiente di allacciamento per mappe ponderate, Rend. Sem. Mat. Univ. Padova 28 (1958), 280–289.

    MATH  MathSciNet  Google Scholar 

  21. G. Darbo, Grado topologico e teoremi di esistenza di punti uniti per trasformazioni plurivalenti di bicelle, Rend. Sem. Mat. Univ. Padova 19 (1950), 371–395.

    MATH  MathSciNet  Google Scholar 

  22. _____, Teoria dell'omologia in una categoria di mappe plurivalenti ponderate, Rend. Sem. Mat. Univ. Padova 28 (1958), 188–220.

    MATH  MathSciNet  Google Scholar 

  23. _____, Sulle coincidenze di mappe ponderate, Rend. Sem. Mat. Univ. Padova 29, 256–270, 1959..

    MATH  MathSciNet  Google Scholar 

  24. _____, Estensione alle mappe ponderate del teorema di Lefschetz sui punti fissi, Rend. Sem. Mat. Univ. Padova 31 (1961), 46–57.

    MATH  MathSciNet  Google Scholar 

  25. A. Dold, Lectures on Algebraic Topology, Springer—Verlag, New York yr 1972; Die Grundlehren der mathematischen Wissenschaften, Band 200.

    MATH  Google Scholar 

  26. _____, The fixed point transfer of fibre-preserving maps, Math. Z. 148(3) (1976), 215–244.

    Google Scholar 

  27. _____, A coincidence-fixed-point index., Enseign. Math. (2) 24 (1978), 41–53.

    Google Scholar 

  28. _____, Ramified coverings, orbit projections and symmetric powers, Math. Proc. Cambridge Philos. Soc. 99 (1986), 65–72.

    Google Scholar 

  29. J. Dugundji, Remark on homotopy inverses, Portugal. Math. 14 (1955), 39–41.

    MATH  MathSciNet  Google Scholar 

  30. S. Eilenberg and D. Montgomery, Fixed point theorems for multi-valued transformations, Amer. J. Math. 68 (1946), 214–222.

    MathSciNet  MATH  Google Scholar 

  31. P. L. Felmer, Periodic solutions of spatially periodic Hamiltonian systems, J. Differential Equations 98 (1992), 143–168.

    Article  MATH  MathSciNet  Google Scholar 

  32. _____, Rotation type solutions for spatially periodic Hamiltonian systems, Nonlinear Anal. 19 (1992), 409–425.

    Article  MATH  MathSciNet  Google Scholar 

  33. P. M. Fitzpatrick, I. Massabò and J. Pejsachowicz, Global several-parameter bifurcation and continuation theorems: a unified approach via complementing maps, Math. Ann. 263 (1983), 61–73.

    Article  MathSciNet  MATH  Google Scholar 

  34. _____, On the covering dimension of the set of solutions of some nonlinear equations, Trans. Amer. Math. Soc. 296 (1986), 777–798.

    Article  MathSciNet  MATH  Google Scholar 

  35. G. Fournier and L. Górniewicz, The Lefschetz fixed point theorem for some non-compact multi-valued maps, Fund. Math. 94) (1977), 245–254.

    MathSciNet  MATH  Google Scholar 

  36. E. M. Friedlander and H. Blaine Lawson Jr., A theory of algebraic cocycles, Ann. of Math. (2) 136 (1992), 361–428.

    Article  MathSciNet  Google Scholar 

  37. K. Fukaya and K. Ono, Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds, The Arnoldfest (Toronto, ON, 1997), Fields Inst. Commun. 24 (1999), Amer. Math. Soc., Providence, RI, 173–190.

    Google Scholar 

  38. F. B. Fuller, Fixed points of multiple-valued transformations, Bull. Amer. Math. Soc. 67 (1961), 165–169.

    MATH  MathSciNet  Google Scholar 

  39. M. Furi, M. Martelli and A. Vignoli, On the solvability of nonlinear operator equations in normed spaces, Ann. Mat. Pura Appl. (4) 124 (1980), 321–343.

    Article  MathSciNet  MATH  Google Scholar 

  40. L. Górniewicz, Homological methods in fixed-point theory of multi-valued maps, Dissertationes Math. (Rozprawy Mat.) 129 (1976), 71.

    Google Scholar 

  41. _____, Topological fixed point theory of multivalued mappings, Mathematics and its Applications, vol. 495, Kluwer Academic Publishers, Dordrecht, 1999.

    Google Scholar 

  42. L. Górniewicz, A. Granas and W. Kryszewski, Sur la méthode de l'homotopie dans la théorie des points fixes pour les applications multivoques II, L'indice dans les ANR-s compacts, C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), 449–452.

    MATH  Google Scholar 

  43. _____, On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighborhood retracts, J. Math. Anal. Appl. 161 (1991), 457–473.

    Article  MathSciNet  MATH  Google Scholar 

  44. L. Górniewicz and M. Lassonde, Approximation and fixed points for compositions of R δ -maps, Topology Appl. 55 (1994), 239–250.

    Article  MathSciNet  MATH  Google Scholar 

  45. L. Górniewicz and P. Nistri, Topological essentiality and nonlinear boundary value control problems, Topol. Methods Nonlinear Anal. 13 (1999), 53–72.

    MathSciNet  MATH  Google Scholar 

  46. L. Górniewicz and M Ślosarski, Topological essentiality and differential inclusions, Bull. Austral. Math. Soc. 45 (1992), 177–193.

    MathSciNet  MATH  Google Scholar 

  47. D. Gottlieb, On realizing Nakaoka's coincidence point transfer as an S-map, Illinois J. Math. 30 (1986), 689–695.

    MATH  MathSciNet  Google Scholar 

  48. D. H. Gottlieb and M. Özaydin, Intersection numbers, transfers, and group actions, Topology Appl. 55 (1994), 87–100.

    Article  MathSciNet  MATH  Google Scholar 

  49. A. Granas, The theory of compact vector fields and some of its applications to topology of functional spacesI, Rozprawy Mat. 30 (1962), 93.

    MATH  MathSciNet  Google Scholar 

  50. _____, Generalizing the Hopf-Lefschetz fixed point theorem for non-compact ANRs, Symposium on Infinite-Dimensional Topology (Louisiana State Univ., Baton Rouge, La., 1967), pp. 119–130; Ann. of Math. Studies 69 (1972), Princeton Univ. Press, Princeton, N. J.

    Google Scholar 

  51. A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer—Verlag, New York, 2003.

    Google Scholar 

  52. V. Guillemin and A. Pollack, Differential Topology, Prentice-Hall Inc., Englewood Cliffs, N.J., 1974.

    MATH  Google Scholar 

  53. B. Halpern, Algebraic topology and set-valued maps, Set-Valued Mappings, Selections and Topological Properties of 2X (Proc. Conf., SUNY, Buffalo, N.Y., 1969), Lecture Notes in Math., vol. 171, Springer, Berlin, 1970, pp. 27–33.

    Google Scholar 

  54. H. Hofer and E. Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher (Birkhäuser Advanced Texts: Basel Textbooks), Birkhäuser Verlag, Basel, 1994.

    Google Scholar 

  55. H. Hopf, On some properties of one-valued transformations of manifolds, Proc. Nat. Acad. Sci. 14 (1928), 206–214.

    MATH  Google Scholar 

  56. W. Hurewicz and H. Wallman, Dimension Theory, Princeton Math. Ser., vol. 4, Princeton University Press, Princeton, N. J., 1941.

    Google Scholar 

  57. R. P. Jerrard, On Knaster's conjecture, Trans. Amer. Math. Soc. 170 (1972), 385–402.

    Article  MATH  MathSciNet  Google Scholar 

  58. _____, Homology with multiple-valued functions applied to fixed points, Trans. Amer. Math. Soc. 213 (1975), 407–427.

    Article  MATH  MathSciNet  Google Scholar 

  59. _____, Erratum to: “Homology with multiple-valued functions applied to fixed points”, (Trans. Amer. Math. Soc., vol. 213 (1975), 407–427), Trans. Amer. Math. Soc. 218 (1976), 406.

    Article  MATH  MathSciNet  Google Scholar 

  60. _____, A stronger invariant for homology theory., Michigan Math. J. 26 (1979), 33–46.

    Article  MATH  MathSciNet  Google Scholar 

  61. _____, Fixed points and product spaces, Houston J. Math. 11 (1985), 191–198.

    MATH  MathSciNet  Google Scholar 

  62. R. Jerrard and M. D. Meyerson, Homotopy with m-functions, Pacific J. Math. 84(2) (1979), 305–318.

    MathSciNet  MATH  Google Scholar 

  63. S. Jodko-Narkiewicz, Topological degree of multivalued weighted mappings, Ph. D. thesis (1989), Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland. (Polish)

    Google Scholar 

  64. R. J. Knill, On the homology of a fixed point set, Bull. Amer. Math. Soc. 77 (1971), 184–190.

    Article  MATH  MathSciNet  Google Scholar 

  65. _____, On the index of isolated closed tori, Differential Topology, Foliations and Gelfand-Fuks Cohomology, (Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, 1976), Lecture Notes in Math., vol. 652, Springer, Berlin, 1978, pp. 196–211.

    Google Scholar 

  66. ______, The Lefschetz fixed point theorem for compact groups, Proc. Amer. Math. Soc. 66 (1977), 148–152.

    Article  MATH  MathSciNet  Google Scholar 

  67. Y. Kodama, On ANR for metric spaces, Sci. Rep. Tokyo Kyoiku Daigaku. Sect. A 5 (1955), 96–98.

    MATH  MathSciNet  Google Scholar 

  68. W. Kryszewski, Some homotopy classification and extension theorems for the class of compositions of acyclic set-valued maps, Bull. Sci. Math. 119(1) (1995), 21–48.

    MATH  MathSciNet  Google Scholar 

  69. _____, The fixed-point index for the class of compositions of acyclic set-valued maps on ANRs, Bull. Sci. Math. 120 (1996), 129–151.

    MATH  MathSciNet  Google Scholar 

  70. _____, Remarks to the Vietoris theorem, Topol. Methods Nonlinear Anal. 8 (1997), 383–405.

    MathSciNet  Google Scholar 

  71. _____, Homotopy properties of set-valued mappings, Ph. D. thesis (1997), Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, habilitation dissertation.

    Google Scholar 

  72. _____, Graph-approximation of set-valued maps on noncompact domains, Topology Appl. 83 (1998), 1–21.

    Article  MATH  MathSciNet  Google Scholar 

  73. _____, Graph-approximation of set valued maps, a survey, Differential Inclusions and Optimal Control, (J. Andres, L. Góorniewicz, P. Nistri), eds.), vol. 2, Lecture Notes in Nonlinear Analysis, Juliusz Schauder Center for Nonlinear Studies, Nicolaus Copernicus University, Toruń, 1998, pp. 223–235.

    Google Scholar 

  74. H. Kurland and J. Robbin, Infinite codimension and transversality, Dynamical Systems — Warwick 1974, (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974; presented to E. C. Zeeman on his fiftieth birthday), vol. 468, Lecture Notes in Math., Springer, Berlin, 1975, pp. 135–150.

    Google Scholar 

  75. S. Lefschetz, Intersections and transformations of complexes and manifolds, Trans. Amer. Math. Soc. 28 (1926), 1–49.

    Article  MATH  MathSciNet  Google Scholar 

  76. _____, On the fixed point formula, Ann. of Math. (2) 38 (1937), 819–822.

    Article  MATH  MathSciNet  Google Scholar 

  77. _____, On coincidences of transformations, Bol. Soc. Mat. Mexicana (2) 2 (1957), 16–25.

    MATH  MathSciNet  Google Scholar 

  78. J. Leray, Sur les équations et les transformations, J. Math. Pures Appl. (9) 24 (1946), 201–248.

    MATH  MathSciNet  Google Scholar 

  79. _____, Théorie des points fixes: indice total et nombre de Lefschetz, Bull. Soc. Math. France 87 (1959), 221–233.

    MATH  MathSciNet  Google Scholar 

  80. E. Magenes, Un'osservazione sui teoremi di esistenza di punti uniti in trasformazioni plurivalenti di una N-cella, Rend. Sem. Mat. Univ. Padova 19 (1950), 108–113.

    MATH  MathSciNet  Google Scholar 

  81. S. Mardešić, Equivalence of singular and Čech homology for ANRs. Application to unicoherence, Fund. Math. 46 (1958), 29–45.

    MathSciNet  MATH  Google Scholar 

  82. S. Mardešić and J. Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam, 1982.

    Google Scholar 

  83. I. Massabo, P. Nistri and J. Pejsachowicz, On the solvability of nonlinear equations in Banach spaces, Fixed Point Theory (Sherbrooke, Que., 1980), Lecture Notes in Math., vol. 886, Springer, Berlin, 1981, pp. 270–299.

    Google Scholar 

  84. I. Massabò and J. Pejsachowicz, On the connectivity properties of the solution set of parametrized families of compact vector fields, J. Funct. Anal. 59 (1984), 151–166.

    Article  MathSciNet  MATH  Google Scholar 

  85. Ch. N. Maxwell, Fixed points of symmetric product mappings, Proc. Amer. Math. Soc. 8 (1957), 808–815.

    Article  MATH  MathSciNet  Google Scholar 

  86. M. C. McCord, Classifying spaces and infinite symmetric products, Trans. Amer. Math. Soc. 146 (1969), 273–298.

    Article  MATH  MathSciNet  Google Scholar 

  87. M. Nakaoka, Coincidence Lefschetz number for a pair of fibre preserving maps, J. Math. Soc. Japan 32(4) (1980), 751–779.

    Article  MATH  MathSciNet  Google Scholar 

  88. P. Nistri, V. V. Obukhovskiĭ and P. Zecca, On the solvability of systems of inclusions involving noncompact operators, Trans. Amer. Math. Soc. 342(2) (1994), 543–562.

    Article  MathSciNet  MATH  Google Scholar 

  89. R. Oliver, A transfer homomorphism for compact Lie group actions, Math. Ann. 260 (1982), 351–374.

    Article  MATH  MathSciNet  Google Scholar 

  90. B. O'Neill, Induced homology homomorphisms for set-valued maps, Pacific J. Math. 7 (1957), 1179–1184.

    MATH  MathSciNet  Google Scholar 

  91. B. O'Neill and E. G. Straus, A fixed point theorem, Proc. Mmer. Math. Soc. 8 (1957), 1148–1151.

    Article  MathSciNet  Google Scholar 

  92. J. Pejsachowicz, The homotopy theory of weighted mappings, Boll. Un. Mat. Ital. B (5) 14 (1977), 702–721.

    MATH  MathSciNet  Google Scholar 

  93. _____, A Lefschetz fixed point theorem for multivalued weighted mappings, Boll. Un. Mat. Ital. A (5) 14 (1977), 391–397.

    MATH  MathSciNet  Google Scholar 

  94. _____, Teoria di omotopia di mappe ponderate, Ph. D. thesis (1973), Tesi di Perfezionamento SNS Pisa, Pisa, Italy.

    Google Scholar 

  95. _____, Relation between the homotopy and the homology theory of weighted mappings, Boll. Un. Mat. Ital. B (5) 15 (1978), 285–302.

    MATH  MathSciNet  Google Scholar 

  96. B. Ralph, A homotopy transfer for finite group actions, Pacific J. Math. 160 (1993), 133–141.

    MATH  MathSciNet  Google Scholar 

  97. R. Schultz, Homological transfers for orbit space projections, Manuscripta Math. 24 (1978), 229–238.

    Article  MATH  MathSciNet  Google Scholar 

  98. G. Scorza Dragoni, Il lemma di Sperner: sue implicazioni negli spazi euclidei equestioni connesse, Contributi del CLISMA 43(2) (1978), 160–170.

    Google Scholar 

  99. B. Segre, Recouvrements de sphères et correspondances entre variétés topologiques, Colloque sur les Questions de Réalité en Géométrie, Liège, 1955, Georges Thone, Liège, 1956, pp. 149–175.

    Google Scholar 

  100. H. W. Siegberg and G. Skordev, Fixed point index and chain approximations, Pacific J. Math. 102 (1982), 455–486.

    MathSciNet  MATH  Google Scholar 

  101. R. Skiba, On the Lefschetz fixed point theorem for multivalued weighted mappings, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 40 (2001), 201–214.

    MATH  MathSciNet  Google Scholar 

  102. _____, Topological essentiality for multivalued weighted mappings, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 41 (2002), 131–145.

    MATH  MathSciNet  Google Scholar 

  103. R. Skiba, Graph-approximation of multivalued weighted maps (to appear).

    Google Scholar 

  104. G. S. Skordev, The multiplicativity property of the fixed point index for multivalued maps, Serdica 15 (1989), 160–170.

    MATH  MathSciNet  Google Scholar 

  105. L. Smith, Transfer and ramified coverings, Math. Proc. Cambridge Philos. Soc. 93 (1983), 485–493.

    Article  MATH  MathSciNet  Google Scholar 

  106. C. Viterbo, Exact Lagrange submanifolds, periodic orbits and the cohomology of free loop spaces, J. Differential Geom. 47 (1997), 420–468.

    MATH  MathSciNet  Google Scholar 

  107. F. von Haeseler, H.-O. Peitgen and G. Skordev, Lefschetz fixed point theorem for acyclic maps with multiplicity, Topol. Methods Nonlinear Anal. 19 (2002), 339–374.

    MathSciNet  MATH  Google Scholar 

  108. F. von Haeseler and G. Skordev, Borsuk-Ulam theorem, fixed point index and chain approximations for maps with multiplicity, Pacific J. Math. 153 (1992), 369–396.

    MathSciNet  Google Scholar 

  109. Ch. S. Vora, Fixed point theorems for certain compact weighted maps of a manifold, Math. Student 46 (1979), 81–86.

    MATH  MathSciNet  Google Scholar 

  110. _____, Some applications of the fixed point theorems for compact weighted maps, Math. Student 46 (1979), 87–99.

    MATH  MathSciNet  Google Scholar 

  111. T. Watanabe, The continuity axiom and the Čech homology, Geometric Topology and Shape Theory (Dubrovnik, 1986), Lecture Notes in Math., vol. 1283, Springer, Berlin, 1987, pp. 221–239.

    Google Scholar 

  112. Th. J. Worosz, Multiple-valued functions and their application to the fixed point properties of product spaces, Bull. Malaysian Math. Soc. (2) 1 (1978), 101–109.

    MATH  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer

About this chapter

Cite this chapter

Pejsachowicz, J., Skiba, R. (2005). Fixed Point Theory of Multivalued Weighted Maps. In: Brown, R.F., Furi, M., Górniewicz, L., Jiang, B. (eds) Handbook of Topological Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3222-6_6

Download citation

Publish with us

Policies and ethics