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Upper bound of second Hankel determinant for a subclass of bi-univalent functions of complex order

Nizami Mustafa
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 783-797|DOI 10.4134/CKMS.c180212

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키워드

analytic functionsunivalent functionsbi-univalent functionsHankel determinant
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초록

In this paper, we introduce and investigate a subclass \linebreak $\Im _{\Sigma }\left( \alpha ,\beta ,{\gamma }\right) $ of analytic and bi-univalent functions of complex order in the open unit disk $U$ in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

Abstract

In this paper, we introduce and investigate a subclass \linebreak $\Im _{\Sigma }\left( \alpha ,\beta ,{\gamma }\right) $ of analytic and bi-univalent functions of complex order in the open unit disk $U$ in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

참고문헌 (36)

  1. O. Altintaş, "Neighborhoods of a class of analytic functions with negative coefficients", Applied Mathematics Letters, 13(3), pp.63~67 (2000), Elsevier BV[DOI]
  2. D. A. Brannan, "Aspects of Contemporary Complex Analysis" (1980), Academic Press, Inc
  3. D. A. Brannan, "On some classes of bi-univalent functions", Math and Appl Kuwait, 18~21 (1985)
  4. David G. Cantor, "Power series with integral coefficients", Bulletin of the American Mathematical Society, 69(3), pp.362~367 (1963), American Mathematical Society (AMS)[DOI]
  5. M. C aꠘglar, "Fekete-Szeg inequalities for subclasses of bi-univalent functions satisfying subordinate conditions", AIP Conference Proceedings, 1726 (2016)[DOI]
  6. Murat ÇAĞLAR, "Second Hankel determinant for certain subclasses ofbi-univalent functions", TURKISH JOURNAL OF MATHEMATICS, 41, pp.694~706 (2017), The Scientific and Technological Research Council of Turkey[DOI]
  7. Murat Cağlar, "Coefficient bounds for new subclasses of bi-univalent functions", Filomat, 27(7), pp.1165~1171 (2013), National Library of Serbia[DOI]
  8. Erhan Deniz, "Certain subclasses of bi-univalent functions satisfying subordinate conditions", Journal of Classical Analysis, (1), pp.49~60 (2012), Element d.o.o.[DOI]
  9. Erhan Deniz, "Second Hankel determinant for bi-starlike and bi-convex functions of order β", Applied Mathematics and Computation, 271, pp.301~307 (2015), Elsevier BV[DOI]
  10. P. L. Duren, "Univalent Functions" (1983), Springer-Verlag
  11. M. Fekete, "Eine Bemerkung Uber Ungerade Schlichte Funktionen", J. London Math. Soc, 8(2), pp.85~89 (1933)[DOI]
  12. B. A. Frasin, "Coecient bounds for certain classes of bi-univalent functions", Hacet. J. Math. Stat, 43(3), pp.383~389 (2014)
  13. B.A. Frasin, "New subclasses of bi-univalent functions", Applied Mathematics Letters, 24(9), pp.1569~1573 (2011), Elsevier BV[DOI]
  14. C. Y. Gao, "Certain subclass of starlike functions", Appl Mat Comput, 187, pp.176~182 (2007)
  15. U. Grenander, "Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences" (1958), University of California Press
  16. Samaneh G. Hamidi, "Faber polynomial coefficient estimates for analytic bi-close-to-convex functions", Comptes Rendus Mathematique, 352(1), pp.17~20 (2014), Elsevier BV[DOI]
  17. A. Janteng, "Hankel determinant for starlike and convex functions", Int. J. Math. Anal. (Ruse), 1(13-16), pp.619~625 (2007)
  18. A. W. Kedzierawski, "Some remarks on bi-univalent functions", Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 39, pp.77~81 (1985)
  19. F. R. Keogh, "A Coefficient Inequality for Certain Classes of Analytic Functions", Proceedings of the American Mathematical Society, 20(1), pp.8~ (1969), JSTOR[DOI]
  20. S. S. Kumar, "Estimates for the initial coecients of bi-univalent functions", Tamsui Oxf. J. Inf. Math. Sci, 29(4), pp.487~504 (2013)
  21. See Keong Lee, "Bounds for the second Hankel determinant of certain univalent functions", Journal of Inequalities and Applications, 2013(1) (2013), Springer Science and Business Media LLC[DOI]
  22. M. Lewin, "On a Coefficient Problem for Bi-Univalent Functions", Proceedings of the American Mathematical Society, 18(1), pp.63~ (1967), JSTOR[DOI]
  23. J. W. Noonan, "On the Second Hankel Determinant of Areally Mean p-Valent Functions", Transactions of the American Mathematical Society, 223, pp.337~ (1976), JSTOR[DOI]
  24. Halit Orhan, "The Fekete–Szegö problem for subclasses of analytic functions defined by a differential operator related to conic domains", Computers & Mathematics with Applications, 59(1), pp.283~295 (2010), Elsevier BV[DOI]
  25. H. Orhan, "Initial coefficient bounds for a general class of bi-univalent functions", Filomat, 29(6), pp.1259~1267 (2015), National Library of Serbia[DOI]
  26. Halit ORHAN, "Bounds for the second Hankel determinant of certain bi-univalent functions", TURKISH JOURNAL OF MATHEMATICS, 40, pp.679~687 (2016), The Scientific and Technological Research Council of Turkey[DOI]
  27. C. Pommerenke, "Univalent Functions" (1975), Vandenhoeck & Ruprecht
  28. Harim Srivastava, "Coefficient estimates for a general subclass of analytic and bi-univalent functions", Filomat, 27(5), pp.831~842 (2013), National Library of Serbia[DOI]
  29. H.M. Srivastava, "Coefficient bounds for a certain class of analytic and bi-univalent functions", Filomat, 29(8), pp.1839~1845 (2015), National Library of Serbia[DOI]
  30. H.M. Srivastava, "Certain subclasses of analytic and bi-univalent functions", Applied Mathematics Letters, 23(10), pp.1188~1192 (2010), Elsevier BV[DOI]
  31. D. L. Tan, "Coecient estimates for bi-univalent functions", Chinese Ann. Math. Ser. A, 5(5), pp.559~568 (1984)
  32. Qing-Hua Xu, "Coefficient estimates for a certain subclass of analytic and bi-univalent functions", Applied Mathematics Letters, 25(6), pp.990~994 (2012), Elsevier BV[DOI]
  33. Qing-Hua Xu, "A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems", Applied Mathematics and Computation, 218(23), pp.11461~11465 (2012), Elsevier BV[DOI]
  34. D.-G. Yang, "A class of analytic functions with missing coecients", Abstr. Appl. Anal, 2011(2011), pp.16~ (2011)[DOI]
  35. P. Zaprawa, "On the Fekete-Szego problem for classes of bi-univalent functions", Bull. Belg. Math. Soc. Simon Stevin, 21(1), pp.169~178 (2014)[DOI]
  36. P. Zaprawa, "Estimates of initial coecients for bi-univalent functions", Abstr. Appl. Anal, 2014, pp.6~ (2014)[DOI]

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