Research article

Geometric properties of harmonic functions associated with the symmetric conjecture points and exponential function

  • Received: 07 June 2020 Accepted: 24 August 2020 Published: 02 September 2020
  • MSC : 30C45, 30C65

  • In this paper, some classes of univalent harmonic functions are introduced by subordination, where the analytic parts of which are exponential starlike (or convex) functions with respect to the symmetric conjecture points. According to the relationships of the analytic part and the co-analytic part, the geometric properties, such as coefficient estimates, distortion theorems, integral expressions, estimates and growth conditions and covering theorem, of the classes are obtained.

    Citation: Lina Ma, Shuhai Li, Huo Tang. Geometric properties of harmonic functions associated with the symmetric conjecture points and exponential function[J]. AIMS Mathematics, 2020, 5(6): 6800-6816. doi: 10.3934/math.2020437

    Related Papers:

  • In this paper, some classes of univalent harmonic functions are introduced by subordination, where the analytic parts of which are exponential starlike (or convex) functions with respect to the symmetric conjecture points. According to the relationships of the analytic part and the co-analytic part, the geometric properties, such as coefficient estimates, distortion theorems, integral expressions, estimates and growth conditions and covering theorem, of the classes are obtained.


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    [1] P. L. Duren, Univalent Functions (Grundlehren der Mathematischen Wissenschaften 259), Springer-Verlag, New York, 1983.
    [2] H. M. Srivastava, S. Owa, Current Topics in Analytic Function Theory, World Scientific, London, 1992.
    [3] M. Fekete, G. Szegö, Eine bemerkung uber ungerade schlichte funktionen, J. Lond. Math. Soc., s1-8 (1933), 85-89.
    [4] W. Ma, D. Minda, A unified treatment of some special classes of univalent functions, In: Proceeding of the Conference on Complex Analysis, International Press, Boston, USA, 1994, 157-169.
    [5] R. M. EL-Ashwah, A. H. Hassan, Fekete-Szegö inequalities for certain subclass of analytic functions defined by using Sălăgean operator, Miskolc Math. Notes, 17 (2017), 827-836. doi: 10.18514/MMN.2017.1495
    [6] W. Koepf, On the Fekete-Szegö problem for close-to-convex functions, P. Am. Math. Soc., 101 (1987), 89-95.
    [7] F. M. Sakar, S. Aytaş, H. Ö. Güney, On The Fekete-Szegö problem for generalized class Mα,γ(β) defined by differential operator, J. Nat. Appl. Sci., Süleyman Demirel University, 20 (2016), 456-459.
    [8] W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Pol. Math., 28 (1973), 297-326. doi: 10.4064/ap-28-3-297-326
    [9] R. Mendiratta, S. Nagpal, V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, B. Malays. Math. Sci. Soc., 38 (2015), 365-386. doi: 10.1007/s40840-014-0026-8
    [10] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. JPN, 11 (1959), 72-75. doi: 10.2969/jmsj/01110072
    [11] R. El-Ashwah, D. Thomas, Some subclasses of closed-to-convex functions, J. Ramanujan Math. Soc., 2 (1987), 85-100.
    [12] J. Clunie, T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Math., 9 (1984), 3-25. doi: 10.5186/aasfm.1984.0905
    [13] P. L. Duren, Harmonic mappings in the plane, Cambridge University Press, England, 2004.
    [14] H. Lewy, On the non-vanishing of the Jacobian in certain one-to-one mappings, B. Am. Math. Soc., 42 (1936), 689-692. doi: 10.1090/S0002-9904-1936-06397-4
    [15] D. Klimek, A. Michalski, Univalent anti-analytic perturbations of convex analytic mappings in the unit disc, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 61 (2007), 39-49.
    [16] I. Hotta, A. Michalski, Locally one-to-one harmonic functions with starlike analytic part, arXiv: 1404.1826, 2014.
    [17] M. Zhu, X. Huang, The distortion theorems for harmonic mappings with analytic parts convex or starlike functions of order β, J. Math., 2015 (2015), 460191.
    [18] G. Kohr, I. Graham, Geometric Function Theory in One and Higher Dimensions, Marcel Dekker, New York, 2003.
    [19] W. Rogosinski, On the coefficients of subordinate functions, P. Lond. Math. Soc., 2 (1945), 48-82.
    [20] Y. Polatoğlu, M. Bolcal, A. Sen, Two-point distortion theorems for certain families of analytic functions in the unit disc, Int. J. Math. Math. Sci., 66 (2003) 4183-4193.
    [21] G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, American Mathematical Society, Rhode Island, 1969.
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