Research article

Comprehensive subclasses of analytic functions and coefficient bounds

  • Received: 12 December 2019 Accepted: 24 March 2020 Published: 05 May 2020
  • MSC : 30C45, 30C80

  • In this paper, we introduce two general subclasses of analytic functions by means of the principle of subordination and investigate the coefficient bounds for functions in these classes. The well-known results are obtained as a corollary of our main results. Especially, we improve the results of Altıntaş and Kılıç [1].

    Citation: Serap Bulut. Comprehensive subclasses of analytic functions and coefficient bounds[J]. AIMS Mathematics, 2020, 5(5): 4260-4267. doi: 10.3934/math.2020271

    Related Papers:

  • In this paper, we introduce two general subclasses of analytic functions by means of the principle of subordination and investigate the coefficient bounds for functions in these classes. The well-known results are obtained as a corollary of our main results. Especially, we improve the results of Altıntaş and Kılıç [1].


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    [1] O. Altıntaş, Ö. Ö Kılıç, Coefficient estimates for a class containing quasi-convex functions, Turk. J. Math., 42 (2018), 2819-2825. doi: 10.3906/mat-1805-90
    [2] W. Ma, D. Minda, A unified treatment of some special classes of univalent functions. In: Proceedings of the conference on complex analysis, Cambridge, MA, (1992), 157-169.
    [3] Y. C. Kim, J. H. Choi, T. Sugawa, Coefficient bounds and convolution properties for certain classes of close-to-convex functions, P. Jpn. Acad. A-Math., 76 (2000), 95-98. doi: 10.3792/pjaa.76.95
    [4] W. Janowski, Some extremal problems for certain families of analytic functions I, Ann. Pol. Math., 28 (1973), 297-326. doi: 10.4064/ap-28-3-297-326
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    [6] R. J. Libera, Some radius of convexity problems, Duke Math. J., 31 (1964), 143-158. doi: 10.1215/S0012-7094-64-03114-X
    [7] K. I. Noor, D. K. Thomas, Quasi-convex univalent functions, Int. J. Math. Math. Sci., 3 (1980), 255-266. doi: 10.1155/S016117128000018X
    [8] W. Rogosinski, On the coefficients of subordinate functions, P. Lon. Math. Soc., 48 (1943), 48-82.
    [9] Q. Xu, Y. Gui, H. M. Srivastava, Coefficient estimates for certain subclasses of analytic functions of complex order, Taiwan. J. Math., 15 (2011), 2377-2386. doi: 10.11650/twjm/1500406441
    [10] K. I. Noor, On quasi-convex functions and related topics, Int. J. Math. Math. Sci., 10 (1987), 241-258. doi: 10.1155/S0161171287000310
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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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