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SOME DISTORTION THEOREMS FOR NEW SUBCLASS OF HARMONIC UNIVALENT FUNCTIONS

  • Received : 2020.03.31
  • Accepted : 2020.10.07
  • Published : 2020.12.25

Abstract

We introduced and studied a new class of harmonic univalent functions on unit disc 𝕌. Also we provided coefficient conditions, extreme points and convolution conditions for that class of harmonic univalent functions.

Keywords

Acknowledgement

Authors appreciate Prof. Ahmad Zireh for his comments. A part of this research was carried out while the third author was visiting the University of Alberta. The author is grateful to his colleagues in the department of mathematics for their kind hosting.

References

  1. A.G. Alanoush, Subclass of harmonic univalent functions associated with the generalized Mittag-Leffler type functions, arXiv:1901.08454v1[math.CV]24Jan2019.
  2. A.K. Al-khafaji, W.G. Atshan, S.S. Abed, On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator, Mathematics, 312(6) (2018), 1-9.
  3. O. Altintas, O. Ozkan and H.M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Letters, 13 (2000), 63--67.
  4. Y. Avci, E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 44 (1990), 1-7.
  5. J. Clunie, T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A.I, 9 (1984) ,3-25.
  6. J. Dziok, Classes of harmonic functions defined by convolution, Bol Soc Mat Mex. 26 (2020), 399-416. https://doi.org/10.1007/s40590-019-00264-0
  7. J. Dziok, S. Yalcin and S. Altinkaya, Subclasses of harmonic univalent functions associated with generalized ruscheweyh operator, Publ. de l'Institut Math. 106 (2019), 19-28. https://doi.org/10.2298/PIM1920019D
  8. K.K. Dixit, S. Porwal, On a subclass of harmonic unnivalent functions, JIPAM, 10(27) (2009), 1-9.
  9. S. Hashemi Sababe and A. Ebadian, Some properties of reproducing kernel Banach and Hilbert spaces, SCMA, 12(1) (2018), 167-177.
  10. S. Hashemi Sababe, A. Ebadian and Sh. Najafzadeh, On 2-inner product spaces and reproducing kernel property, TKJM, 49(2) (2018), 143-153.
  11. W. Hengartner, G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc., 299(1) (1987), 1-31. https://doi.org/10.1090/S0002-9947-1987-0869396-9
  12. Z.J. Jakubowski, W. Majchrzak, K. Skalska, Harmonic mappings with a positive real part, (1993).
  13. M. Ozturk, S. Yalcin, On univalent harmonic functions, J. Inequal. Pure Appl. Math., 3(4) (2002), 1--8.
  14. S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), 521-528. https://doi.org/10.1090/S0002-9939-1981-0601721-6
  15. T.M. Seoudy, M.K. Aouf, Several properties of certain classes of univalent harmonic functions, Afr. Mat., 26 (2014), 627-636 . https://doi.org/10.1007/s13370-014-0235-1
  16. T.M. Seoudy, Some Properties Of Certain Classes Of Harmonic Univalent Functions, Al.i. CUZA, (2013), 1-10 .
  17. M.M. Shabani and S. Hashemi Sababe, On some classes of spiral-like functions defined by the Salagean operator, Korean J. Math. 28 (2020), 137-147. https://doi.org/10.11568/kjm.2020.28.1.137