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Fixed Points of Some Real and Complex Functions

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Abstract

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

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References

  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. Bailey, D.F.: Krasnoselski’s theorem on the real line. Am. Math. Mon. 81, 506–507 (1974)

    Article  MathSciNet  Google Scholar 

  3. Baxter, G., Joichi, J.T.: On functions that commute with full functions. Nieuw Arch. Wiskd. 3(XII), 12–18 (1964)

    MathSciNet  MATH  Google Scholar 

  4. Bergweiler, W.: On the existence of fix points of composite meromorphic functions. Proc. Am. Math. Soc. 114, 879–880 (1992)

    Article  Google Scholar 

  5. Boyce, W.M.: Commuting functions with no common fixed point. Trans. Am. Math. Soc. 137, 77–92 (1969)

    Article  MathSciNet  Google Scholar 

  6. Cano, J.: Fixed points for a class of commuting mappings on an interval. Proc. Am. Math. Soc. 86, 336–338 (1982)

    Article  MathSciNet  Google Scholar 

  7. Chu, S.C., Moyer, R.D.: On continuous functions commuting functions and fixed points. Fundam. Math. 59, 91–95 (1966)

    Article  MathSciNet  Google Scholar 

  8. Ciesielski, K., Pogoda, Z.: On ordering the natural numbers or the Sharkovski theorem. Am. Math. Mon. 115, 159–165 (2008)

    Article  MathSciNet  Google Scholar 

  9. Cohen, H.: On fixed points of commuting function. Proc. Am. Math. Soc. 15, 293–296 (1964)

    Article  MathSciNet  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  Google Scholar 

  13. Denjoy, A.: Sur l’iteration des fonctions analytiques. C.R. Acad. Sci. Paris 182, 255–257 (1926)

    MATH  Google Scholar 

  14. Du, B.S.: A simple proof of Sharkovsky’s theorem revisited. Am. Math. Mon. 114, 152–155 (2007)

    Article  MathSciNet  Google Scholar 

  15. Ellis, R.: Distal transformation groups. Pac. J. Math. 8, 401–405 (1958)

    Article  MathSciNet  Google Scholar 

  16. Gross, F.: On factorization of meromorphic functions. Trans. Am. Math. Soc. 131, 215–222 (1968)

    Article  MathSciNet  Google Scholar 

  17. Huneke, J.P.: On common fixed points of commuting continuous functions on an interval. Trans. Am. Math. Soc. 139, 371–381 (1969)

    Article  MathSciNet  Google Scholar 

  18. Isbell, J.R.: Commuting mappings of trees, research problem # 7. Bull. Am. Math. Soc. 63, 419 (1957)

    Article  Google Scholar 

  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. Krasnoselskii, M.A.: Two remarks on the method of sequential approximations. Usp. Mat. Nauk 10, 123–127 (1955)

    Google Scholar 

  21. Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Mon. 103, 985–992 (1975)

    Article  MathSciNet  Google Scholar 

  22. May, R.B.: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)

    Article  Google Scholar 

  23. Numakura, K.: On bicompact semigroups. Math. J. Okayama Univ. 1, 99–108 (1952)

    MathSciNet  MATH  Google Scholar 

  24. Ritt, J.F.: Permutable rational functions. Trans. Am. Math. Soc. 25, 399–448 (1923)

    Article  MathSciNet  Google Scholar 

  25. Schirmer, H.: A topologist’s view of Sharkovsky’s theorem. Houst. J. Math. 11, 385–394 (1985)

    MathSciNet  MATH  Google Scholar 

  26. Schwartz, A.J.: Common periodic points of commuting functions. Mich. Math. J. 12, 353–355 (1965)

    Article  MathSciNet  Google Scholar 

  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. Shields, A.L.: On fixed points of analytic functions. Proc. Am. Math. Soc. 15, 703–706 (1964)

    Article  MathSciNet  Google Scholar 

  29. Suffridge, T.J.: Common fixed points of commuting holomorphic maps of the hyperball. Mich. Math. J. 21, 309–314 (1974)

    MathSciNet  MATH  Google Scholar 

  30. Thron, W.J.: Sequences generated by iteration. Trans. Am. Math. Soc. 96, 38–53 (1960)

    Article  MathSciNet  Google Scholar 

  31. Wallace, A.D.: The structure of topological semigroups. Bull. Am. Math. Soc. 61, 95–112 (1955)

    Article  MathSciNet  Google Scholar 

  32. Wolff, J.: Sur l’iteration des functions holomorphe. C.R. Acad. Sci. Paris 182, 42–43 (1926). 200-201

    MATH  Google Scholar 

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Correspondence to P. V. Subrahmanyam .

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Subrahmanyam, P.V. (2018). Fixed Points of Some Real and Complex Functions. In: Elementary Fixed Point Theorems. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-3158-9_2

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