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Fixed Points of Some Real and Complex Functions

  • P. V. SubrahmanyamEmail author
Chapter
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Abstract

This chapter highlights some fixed point theorems for certain real and complex functions.

References

  1. 1.
    Ahlfohrs, L.V.: Complex Analysis an Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd edn. McGraw-Hill Book Co., New York (1978)Google Scholar
  2. 2.
    Bailey, D.F.: Krasnoselski’s theorem on the real line. Am. Math. Mon. 81, 506–507 (1974)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Baxter, G., Joichi, J.T.: On functions that commute with full functions. Nieuw Arch. Wiskd. 3(XII), 12–18 (1964)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Bergweiler, W.: On the existence of fix points of composite meromorphic functions. Proc. Am. Math. Soc. 114, 879–880 (1992)CrossRefGoogle Scholar
  5. 5.
    Boyce, W.M.: Commuting functions with no common fixed point. Trans. Am. Math. Soc. 137, 77–92 (1969)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Cano, J.: Fixed points for a class of commuting mappings on an interval. Proc. Am. Math. Soc. 86, 336–338 (1982)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Chu, S.C., Moyer, R.D.: On continuous functions commuting functions and fixed points. Fundam. Math. 59, 91–95 (1966)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ciesielski, K., Pogoda, Z.: On ordering the natural numbers or the Sharkovski theorem. Am. Math. Mon. 115, 159–165 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cohen, H.: On fixed points of commuting function. Proc. Am. Math. Soc. 15, 293–296 (1964)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Cohen, H., Hachigian, J.: On iterates of of continuous functions on a unit ball. Proc. Am. Math. Soc. 408–411 (1967)Google Scholar
  11. 11.
    Conway, J.B.: Functions of One Complex Variable, Springer International Student Edition. Authorized reprint of the original edition published by Springer, New York, Narosa Publishing House Reprint (2nd edn.) ninth reprint (1990)Google Scholar
  12. 12.
    Coven, E.M., Hedlund, G.A.: Continuous maps of the interval whose periodic points form a closed set. Proc. Am. Math. Soc. 79, 127–133 (1980)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Denjoy, A.: Sur l’iteration des fonctions analytiques. C.R. Acad. Sci. Paris 182, 255–257 (1926)zbMATHGoogle Scholar
  14. 14.
    Du, B.S.: A simple proof of Sharkovsky’s theorem revisited. Am. Math. Mon. 114, 152–155 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Ellis, R.: Distal transformation groups. Pac. J. Math. 8, 401–405 (1958)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Gross, F.: On factorization of meromorphic functions. Trans. Am. Math. Soc. 131, 215–222 (1968)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Huneke, J.P.: On common fixed points of commuting continuous functions on an interval. Trans. Am. Math. Soc. 139, 371–381 (1969)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Isbell, J.R.: Commuting mappings of trees, research problem # 7. Bull. Am. Math. Soc. 63, 419 (1957)CrossRefGoogle Scholar
  19. 19.
    Jachymski, J.: Equivalent conditions involving common fixed points for maps on the unit interval. Proc. Am. Math. Soc. 124, 3229–3233 (1996)Google Scholar
  20. 20.
    Krasnoselskii, M.A.: Two remarks on the method of sequential approximations. Usp. Mat. Nauk 10, 123–127 (1955)Google Scholar
  21. 21.
    Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Mon. 103, 985–992 (1975)MathSciNetCrossRefGoogle Scholar
  22. 22.
    May, R.B.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)CrossRefGoogle Scholar
  23. 23.
    Numakura, K.: On bicompact semigroups. Math. J. Okayama Univ. 1, 99–108 (1952)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Ritt, J.F.: Permutable rational functions. Trans. Am. Math. Soc. 25, 399–448 (1923)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Schirmer, H.: A topologist’s view of Sharkovsky’s theorem. Houst. J. Math. 11, 385–394 (1985)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Schwartz, A.J.: Common periodic points of commuting functions. Mich. Math. J. 12, 353–355 (1965)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Sharkovsky, A.N.: Coexistence of cycles of a continuous mapping of the line into iteslf. Ukr. Math. J. 16, 61–71 (1964)Google Scholar
  28. 28.
    Shields, A.L.: On fixed points of analytic functions. Proc. Am. Math. Soc. 15, 703–706 (1964)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Suffridge, T.J.: Common fixed points of commuting holomorphic maps of the hyperball. Mich. Math. J. 21, 309–314 (1974)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Thron, W.J.: Sequences generated by iteration. Trans. Am. Math. Soc. 96, 38–53 (1960)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Wallace, A.D.: The structure of topological semigroups. Bull. Am. Math. Soc. 61, 95–112 (1955)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wolff, J.: Sur l’iteration des functions holomorphe. C.R. Acad. Sci. Paris 182, 42–43 (1926). 200-201zbMATHGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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