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2014 | 12 | 9 | 1337-1348
Tytuł artykułu

Epsilon Nielsen coincidence theory

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We construct an epsilon coincidence theory which generalizes, in some aspect, the epsilon fixed point theory proposed by Robert Brown in 2006. Given two maps f, g: X → Y from a well-behaved topological space into a metric space, we define µ ∈(f, g) to be the minimum number of coincidence points of any maps f 1 and g 1 such that f 1 is ∈ 1-homotopic to f, g 1 is ∈ 2-homotopic to g and ∈ 1 + ∈ 2 < ∈. We prove that if Y is a closed Riemannian manifold, then it is possible to attain µ ∈(f, g) moving only one rather than both of the maps. In particular, if X = Y is a closed Riemannian manifold and idY is its identity map, then µ ∈(f, idY) is equal to the ∈-minimum fixed point number of f defined by Brown. If X and Y are orientable closed Riemannian manifolds of the same dimension, we define an ∈-Nielsen coincidence number N ∈(f, g) as a lower bound for µ ∈(f, g). Our constructions and main results lead to an epsilon root theory and we prove a Minimum Theorem in this special approach.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
9
Strony
1337-1348
Opis fizyczny
Daty
wydano
2014-09-01
online
2014-05-08
Twórcy
Bibliografia
  • [1] Brooks R.B.S., On removing coincidences of two maps when only one, rather than both of them, may be deformed by a homotopy, Pacific J. Math., 1972, 40, 45–52 http://dx.doi.org/10.2140/pjm.1972.40.45
  • [2] Brown R.F., The Lefschetz Fixed Point Theorem, Scott, Foresman, Glenview-London, 1971
  • [3] Brown R.F., Epsilon Nielsen fixed point theory, Fixed Point Theory Appl., 2006, Special Issue, #29470
  • [4] do Carmo M.P., Riemannian Geometry, Math. Theory Appl., Birkhäuser, Boston, 1992
  • [5] Cotrim F.S., Homotopias Finitamente Fixadas e Pares de Homotopias Finitamente Coincidentes, M.Sc. thesis, Universidade Federal de São Carlos, São Carlos, 2011
  • [6] Gonçalves D.L., Coincidence theory, In: Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 3–42 http://dx.doi.org/10.1007/1-4020-3222-6_1
  • [7] Milnor J., Morse Theory, Ann. of Math. Stud., 51, Princeton University Press, Princeton, 1963
  • [8] Munkres J.R., Topology, 2nd ed., Prentice-Hall, Englewood Cliffs, 2000
  • [9] Vick J.W., Homology Theory, 2nd ed., Grad. Texts in Math., 145, Springer, New York, 1994 http://dx.doi.org/10.1007/978-1-4612-0881-5
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0412-3
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