Bibliography of Sendov Conjecture

  1. Aziz, A.: On the zeros of a polynomial and its derivative, Bull. Austr. Math. Soc. 31, n. 4 (1985), 245 – 255.
  2. Bidkham M. and K. K. Dewan: Inequalities for a polynomial and its derivatives, J. Math. Anal. Appl. 166 (1992), 319 324.
  3. Bojanov, B. D.: The conjecture of Sendov about the critical points of polynomials, Fiz. Mat. Spisanie (1984), 140 – 150 (in Bulgarian).
  4. Bojanov, B. D., Q. I. Rahman and J. Szynal: On a conjecture of Sendov about the critical points of a polynomial, Math. Z. 190 (1985), 281 – 285.
  5. Bojanov, B. D., Q. I. Rahman and J. Szynal: On a conjecture about the critical points of a polynomial, In: Delay Equations, Approximation and Application (G. Meinardus and G N\”{u}rnberg, Eds.), ISNM 74, Birkh\”{a}user Verlag, Basel, 1985, 83 – 93.
  6. Borcea, J.: Dualities, affine vertex operator algebras, and geometry of complex polynomials, Dissertation, Lund University, 1988.
  7. Borcea, J.: On the Sendov conjecture for polynomials with at most six distinct zeros, J. Math. Anal. Appl. 200, n. 1 (1996), 182 – 206.
  8. Borcea, J.: The Sendov conjecture for polynomials with at most seven distinct roots, Analysis 16 (1996), 137 – 159.
  9. Borcea, J.: Two approaches to Sendov’s conjecture, Arhiv der Mathematik 71, n. 1 (1998), 46 – 54.
  10. Brannan, D. A.: On univalent polynomials and related functions, Thesis, University of London, 1967.
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  12. Brown, J. E.: On the Ilieff-Sendov conjecture, Pacific J. Math. 135 (1988), 223 – 232.
  13. Brown, J. E.: On the Sendov conjecture for sixth degree polynomials, Proc. Amer. Math. Soc. 113, n. 4 (1991), 939 – 946.
  14. Brown, J. E.: A proof of the Sendov conjecture for polynomials of degree seven. Complex Variables Theory Appl. 33, n. 1-4 (1997), 75–95.
  15. Brown, J. E.: On the Sendov’s Conjecture for polynomials with real critical points, Contemporary Mathematics 252 (1999), 49 – 62.
  16. Brown, J. E. and G. Xiang: Proof of the Sendov conjecture for polynomials of degree at most eight, J. Math. Anal. Appl. 232, n. 2 (1999), 272–292.
  17. Byrne, A.: Some results for Sendov conjecture, J. Math Anal. Appl. 199 (1996), 754 – 768.
  18. Byrne, A.: Results Pertaining to the Sendov conjecture, J. Math Anal. Appl. 212 (1997), 333 – 342.
  19. Cohen, G. L. and G. H. Smith: A proof of Iliev’s conjecture for polynomials with four zeros, Elemente d. Math. 43 (1988), 18 – 21.
  20. Cohen, G. L. and G. H. Smith: A simple verification of Iliev’s conjecture for polynomials with three zeros, Amer. Math. Mountly 95 (1988), 734 – 737.
  21. Dimitrov, D. G.: On a conjecture of Sendov, C. R. Acad. Bulg. Sci. 36, n. 5 (1983), 561 – 563.
  22. Dronka, J.: On the zeros of a polynomial and its derivative. Zeszyty Nauk. Politech. Rzeszowskiej. Mat. Fiz. n. 9 (1989), 33–36.
  23. Dronka, J.; Sok\’{o}l, J.: On the location of critical points of some complex polynomials. Demonstratio Math. 32, n. 2 (1999), 297–302.
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  25. Goodman, A. W.: On the derivative with respect to a point, Proc. Amer. Math. Soc. 101 (1987), no. 2, 327–330.
  26. Goodman, A. W.: On the zeros of the derivative of a rational function, J. Math. Anal. Appl. 132 (1988), no. 2, 447–452.
  27. Goodman, A. G., Q. I. Rahman and J. Ratti: On the zeros of a polynomial and its derivative, Proc. Amer. Math. Soc. 21 (1969), 273 – 274.
  28. Hayman, W. K.: Research Problems in Function Theory, Althlone Press, London, 1967.
  29. Istr\v{a}\c{t}escu, V. I.: Zeros of Problems, Selected Topics, Romania, 1988.
  30. Joyal, A.: On the zeros of a polynomial and its derivative, J. Math. Anal. Appl. 25 (1969), 315 – 317.
  31. Kasten, Volker: The Sendov conjecture and the maximum principle, Workshop on Complex Analysis (Lublin, 1994), Ann. Univ. Mariae Curie-Sk\l odowska Sect. A 48 (1994), 52–59.
  32. Katsoprinakis, E. S.: On the Sendov-Ilieff conjecture, Preprint n. 29, 1994, University of Crete.
  33. Katsoprinakis, E. S.: On the Sendov-Ilieff conjecture, Bull. London Math. Soc. 24 (1992), 449 – 455.
  34. Katsoprinakis, E. S.: Erratum to “On the Sendov-Ilieff conjecture”, Bull. London Math. Soc. 28 (1996), 605 – 612.
  35. Kjurkchiev, N.: On Sendov’s conjecture, C. R. Acad. Bulg. Sci. 45, n. 10 (1992), 21 – 22.
  36. Kumar, S. and B. G. Shenoy: A note on the Ilyeff-Sendov conjecture, Indian J. Pure Appl. Math. 21, n. 11 (1990), 981–983.
  37. Kumar, S. and B. G. Shenoy: On some counterexamples for a conjecture in geometry of polynomials, Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz. n. 12 (1991), 47 – 51.
  38. Kumar, S. and B. G. Shenoy: On the Sendov-Ilieff conjecture for polynomials with at most five zeros, J. Math. Anal. Appl. 171 (1992), 595 – 600.
  39. Kumar, S. and B. G. Shenoy: A note on the Ilyeff-Sendov conjecture for polynomials of arbitrary degree with multiple zeros, Indian J. Pure Appl. Math. 25, n. 5 (1994), 489 – 495.
  40. Lagrevin, M.: Sphere de Riemann at G\’eom\’etrie des polynomials, Lect. Notes Math. 1415 (1990), 138 – 150.
  41. Marden, A. and P. Marden: Morris Marden (1905 – 1991), J. Complex Variables 26, (1994), 183 -186.
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  43. Marden, M.: Much ado about nothing, Amer. Math. Mounthly 83 (1976), 788 – 798.
  44. Marden, M.: On the critical points of a polynomial, Tensor (N. S.) 39 (1982), 124 – 126.
  45. Marden, M.: Conjectures on the critical points of a polynomial, Amer. Math. Mounthly 90 (1983), 267 – 276.
  46. Marden, M.: The search for a Roll’s theorem in the complex plain, Amer. Math. Mounthly 92 (1984), 643 – 650.
  47. McCoy, T. L.: A principle of O. Sz\’{a}sz and the Sendov-Ilyeff problem for polynomials near $z^n – 1$, Complex Variables Theory Appl. 35, n. 4 (1998), 121–155.
  48. Meir, A. and A. Sharma: On Ilieff’s conjeture, Pacific J. Math. 31 (1969), 459 – 467.
  49. Miller, M. J.: Maximal polynomials and the Ilieff-Sendov conjeture, Trans. Amer. Math. Soc. 321 (1990), 285 – 303.
  50. Miller, M. J.: Continuous independence and the Ilieff-Sendov conjeture, Proc. Amer. Math. Soc. 115 n. 1 (1992), 79 – 83.
  51. Miller, M. J.: On Sendov’s conjecture for roots near the unit circle, J. Math. Anal. Appl. 175 (1993), 632 – 639.
  52. Miller, M. J.: Some Maximal Polynomials Must Be Nonreal, J. Math. Anal. Appl., 214 (1997), 283 – 291.
  53. Milovanovi\’c, G. V., D. S. Mitrinovi\’c and Th. M. Rassias: Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapure, 1994. 78 – 83.
  54. Petersen, B. E.: Convex Hull, Lucas Theorem, Aziz’s Theorem and the Sendov – Ilieff Conjecture, Feb. 29, 2000. \\ \verb|http://www.peak.org/~petersen/maple/maple_notes.html|
  55. Pflug, P. and G. Schmieder: Remarks on Ilieff-Sendov Problem, Annals Univ. Mariae Curie-Sklodowska Lublin, Poland, XLVIII n. 9, (1994), 98 – 105.
  56. Phelps, D. and R. S. Rodriguez: Some properties of extremal polynomials for the Ilieff conjecture, Kodai Math. Sem. Rep. 24 (1972), 172 – 175.
  57. Qazi, M. A.: On the maximum modulus of polynomials, Proc. Amer. Math. Soc. 115 (1992), 337 – 343.
  58. Rahman, Q. I.: On the zeroes of a polynomial and its derivative, Pacific J. Math. 41 (1972), 525 – 528.
  59. Rahman, Q. I. and Q. M. Tariq: On a problem related to the conjecture of Sendov about the critical points of a polynomial, Canad. Math. Bull, 30, n. 4 (1987), 476 – 480.
  60. Rassias, Th. M.: On certain properties of polynomials and their derivative. Topics in mathematical analysis, 758–802, Ser. Pure Math., 11, World Sci. Publishing, Teaneck, NJ, 1989.
  61. Rassias, Th. M.: Zeros of polynomials and their derivative, Rev. Roumaine Math. Purres Appl. 36 (1991), 441 – 448.
  62. Rassias, Th. M. and H. M. Srivastava: Some recent advances in the theory of the zeros and critical points of a polynomial, In: Topics in Polynomials of One and Several Variables and Their Applications; A mathematical Legacy of P. L Chebyshev (1821 1894) (Th. M. Rassias, H. M. Srivastava and A. Yanushauskas, Eds.), World Scientific, Singapure, 1993, 463 – 481.
  63. Rubinstein, Z.: On a problem of Ilieff, Pacific J. Math. 26 (1968), 159 – 161.
  64. Saff, E. B. and J. B. Twomey: A note on the location of critical points of polynomials, Proc. Amer. Math. Soc. 27, n. 2 (1971), 303 – 308.
  65. Schmeisser, G.: Bemerkungen zu einer Vermutung von Ilieff, Math. Z. 111 (1969), 121 – 125.
  66. Schmeisser, G: Zur Lage der Kritichen puncte eines polynoms, Rend. Sem. Mat. Univ. Padova 46 (1971), 165 -173.
  67. Schmeisser, G: On Ilieff’s conjecture, Math. Z. 156 (1977), 165 – 173.
  68. Schmieder, G. and G. Kurth: Uber Polynome and deren Ableitungen, Math. Semesterberichte 37 (1990), 265 – 270.
  69. Schmieder, Gerald: Der Satz von Rolle im Komplexen. Math. Semesterber 44, n. 2 (1997), 109– 120.
  70. Schmieder, G.: Location of Critical Points for Polynomials, Proc. Comp. Methods in Function Theory (CMFT’97) (1999), 497 – 504.
  71. Schmieder, G.: Die Vermutung von Sendov -eine actuelles mathematisches Problem, Presse\&Kommunika, Carl von Ossietzky Univ. Oldenburg, 1999.
  72. Sendov, Bl.: On the cditical points of a polynomial, East J. on Approximations, 1, n. 2 (1995), 255 – 258.
  73. Stoyanov, J.: Some problems from the analysis, resolved by the methods of the probability theory, Mathemmatics today, “Visha Shkola”, Kiev, 1993, 176 – 194 (in Russian).
  74. Tariq, Q. M.: On the zeros of a polynomial and its derivative, J. Univ. Kuwait (Sci.) 13, (1986), 17 – 19.
  75. Tariq, Q. M.: On the zeros of a polynomial and its derivative II, J. Univ. Kuwait (Sci.) 13, (1986), 151 – 155.
  76. Todorov, P. G.: A natural verification of the Sendov conjecture for the canonical cubic equation and other results for the location of its roots, Bull. de la Classe des Sciences, VII (1996), 387 – 403.
  77. Todorov, P. G.: A natural verification of Sendov’s conjecture for the canonical cubic equation. C. R. Acad. Bulgare Sci. 49, n. 9-10 (1996), 15–18.
  78. Vernon, S.: On the critical points of polynomials, Proc. Roy. Irish Acad. Sect. A, 78 (1978), 195 – 198.
  79. V\^aj\^atu, V. and A. Zaharescu: Ilyeff’s conjecture on a corona. Bull. London Math. Soc. 25, n. 1 (1993), 49 – 54.
  80. Yadrenko, M. I.: The problem of Blagovest Sendov for the critical points of the polynomials, U sviti matematiki, 1, n. 2 (1995), 44- 45 (in Ukrain).
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