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THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS

Deepak Bansal|Sudhananda Maharana|Jugal Kishore Prajapat
대한수학회 (The Korean Mathematical Society)|2015.11|대한수학회지 (Journal of the KMS)|제52권 제6호|pp. 1139-1148

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참고문헌

키워드

analytic functionsstarlike functionsunivalent functionclose-to-convex functionsHankel determinantFekete-Szeg¨o functional
주제분류수학

초록

The estimate of third Hankel determinant H3,1(f) = [수식] of the analytic function f(z) = z + a2z2 + a3z3 + · · · , for which ℜ(1 + zf′′(z)/f′(z)) > −1/2 are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

Abstract

The estimate of third Hankel determinant H3,1(f) = [수식] of the analytic function f(z) = z + a2z2 + a3z3 + · · · , for which ℜ(1 + zf′′(z)/f′(z)) > −1/2 are investigated. The corrected version of a known results [2, Theorem 3.1 and Theorem 3.3] are also obtained.

참고문헌 (28)

  1. H. R. Abdel-Gawad, "The Fekete-Szeg¨o problem for strongely closeto-convex functions", Proc. Amer. Math. Soc, 114(2), pp.345~349 (1992)
  2. K. O. Babalola, "On third order Hankel determinant for some classes of univalent functions", Inequal. Theory Appl, 6, pp.1~7 (2010)
  3. K. O. Babalola, "Advances in Inequalities for Series" (2008), Nova Science Publishers
  4. D. Bansal, "Upper bound of second Hankel determinant for a new class of analytic functions", Appl. Math. Lett, 26(1), pp.103~107 (2013)
  5. B. Bhowmik, "On the Fekete-Szeg¨o problem for concave univalent functions", J. Math. Anal. Appl, 373(2), pp.432~438 (2011)
  6. D. G. Cantor, "Power series with integral coefficients", Bull. Amer. Math. Soc, 69, pp.362~366 (1963)
  7. P. L. Duren, "Univalent Functions", Grundlehren der Mathematischen Wissenschaften, 259 (1983), Springer-Verlag
  8. R. Ehrenborg, "The Hankel determinant of exponential polynomials", Amer. Math. Monthly, 107(6), pp.557~560 (2000)
  9. M. Fekete, "Eine Benberkung uber ungerada Schlichte funktionen", J. Lond. Math. Soc, 8, pp.85~89 (1933)
  10. W. K. Hayman, "On the second Hankel determinant of mean univalent functions", Proc. Lond. Math. Soc. (3), 18, pp.77~94 (1968)
  11. A. Janteng, "Coefficient inequality for a function whose derivative has a positive real part", J. Inequal. Pure Appl. Math, 7(2), pp.5~ (2006)
  12. F. R. Keogh, "A coefficient inequality for certain classes of analytic functions", Proc. Amer. Math. Soc, 20, pp.8~12 (1969)
  13. Y. C. Kim, "Coefficient bounds and convolution properties for certain classes of close-to-convex functions", Proc. Japan Acad. Ser. A Math. Sci, 76(6), pp.95~98 (2000)
  14. W. Koepf, "On the Fekete-Szeg¨o problem for close-to-convex functions", Proc. Amer. Math. Soc, 101(1), pp.89~95 (1987)
  15. B. Kowalczyk, "The Fekete-Szeg¨o inequality for close-to-convex functions with respect to a certain starlike function dependent on a real parameter", J. Inequal. Appl, 2014, pp.16~ (2014)
  16. S. K. Lee, "Bounds for the second Hankel determinant of certain univalent functions", J. Inequal. Appl, 2013, pp.17~ (2013)
  17. J. L. Li, "some questions and conjectures in the theory of univalent functions", Rocky Mountain J. Math, 28(3), pp.1035~1041 (1998)
  18. R. J. Libera, "Early coefficients of the inverse of a regular convex function", Proc. Amer. Math. Soc, 85(2), pp.225~230 (1982)
  19. R. J. Libera, "Coefficient bounds for the inverse of a function with derivatives", P, Proc. Amer. Math. Soc, 87(2), pp.251~257 (1983)
  20. R. R. London, "Fekete-Szeg¨o inequalities for close-to-convex functions", Proc. Amer. Math. Soc, 117(4), pp.947~950 (1993)
  21. T. H. Macgregor, "Functions whose derivative has a positive real part", Trans. Amer. Math. Soc, 104, pp.532~537 (1962)
  22. J. W. Noonan, "On the second Hankel determinant of areally mean p-valent functions", Trans. Amer. Math. Soc, 223, pp.337~346 (1976)
  23. K. I. Noor, "Higher order close-to-convex functions", Math. Japon, 37(1), pp.1~8 (1992)
  24. R. Parvatham, "New Trends in Geometric Function Theory and Application" (1981), World Scientific Publishing Company
  25. C. Pommerenke, "On the coefficients and Hankel determinant of univalent functions", J. Lond. Math. Soc, 41, pp.111~122 (1966)
  26. S. Ponnusamy, "Radius of convexity of partial sums of functions in the close-to-convex family", Nonlinear Anal, 95, pp.219~228 (2014)
  27. M. Raza, "Upper bound of the third Hankel determinant for a class of analytic functions related with Lemniscate of Bernoulli", J. Inequal. Appl, 2013, pp.8~ (2013)
  28. T. V. Sudharsana, "Third Hankel determinant for a subclass of analytic univalent functions", Malaya J. Mat, 2(4), pp.438~444 (2014)

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