호남수학학술지 (Honam Mathematical Journal)

  • 제46권1호
  • /
  • Pages.120-135
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  • 2024
  • /
  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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SUFFICIENT CONDITIONS FOR ANALYTIC FUNCTIONS TO BE STARLIKE OF RECIPROCAL ORDER

  • Shalu Yadav (Department of Mathematics, National Institute of Technology, Tiruchirappalli) ;
  • V. Ravichandran (Department of Mathematics, National Institute of Technology, Tiruchirappalli)
  • 투고 : 2023.07.31
  • 심사 : 2023.09.25
  • 발행 : 2024.03.20
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초록

A normalized analytic function f, defined on the unit disk 𝔻, is starlike of reciprocal order α > 1 if the real part of f(z)/(zf'(z)) is less than α for all z ∈ 𝔻. By utilizing the theory of differential subordination, we establish several sufficient conditions for analytic functions defined on 𝔻 to be starlike of reciprocal order. Additionally, we investigate the conditions under which the function f(z)/(zf'(z)) is subordinate to the function 1 + (α - 1)z. This subordination, in turn, is sufficient for the function f to be starlike of reciprocal order α > 1.

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과제정보

The first author is supported by an institute fellowship from NIT Trichy.

참고문헌

  1. T. Al-Hawary and B. A. Frasin, Coefficient estimates and subordination properties for certain classes of analytic functions of reciprocal order, Stud. Univ. Babes-Bolyai Math. 63 (2018), no. 2, 203-212.  https://doi.org/10.24193/subbmath.2018.2.04
  2. B. A. Frasin and M. A. Sabri, Sufficient conditions for starlikeness of reciprocal order, Eur. J. Pure Appl. Math. 10 (2017), no. 4, 871-876. 
  3. B. A. Frasin, Y. Talafha, and T. Al-Hawary, Subordination results for classes of functions of reciprocal order, Tamsui Oxf. J. Inf. Math. Sci. 30 (2014), 81-89. 
  4. B. B. Janani and V. Ravichandran, Sufficient conditions for functions to be meromorphic starike of reciprocal order α, to apeear in J. Analysis. 
  5. P. G. Krishnan, and V. Ravichandran and P. Saikrishnan, Reciprocal starlikeness of meromorphic functions, preprint. 
  6. V. Kumar, S. Kumar, and N. E. Cho, Coefficient functionals for starlike functions of reciprocal order, Thai J. Math. 20 (2022), no. 3, 1183-1197. 
  7. S. Madhumitha and V. Ravichandran, Sufficient conditions for starlikeness of reciprocal order, to appear in Korean J. Math. 
  8. S. Maharana and D. Bansal, Coefficient estimates for the family of starlike and convex functions of reciprocal order, Afr. Mat. 33 (2022), no. 1, Paper No. 25, 10 pp. 
  9. S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), no. 2, 157-172.  https://doi.org/10.1307/mmj/1029002507
  10. S. S. Miller and P. T. Mocanu, On some classes of first-order differential subordinations, Michigan Math. J. 32 (1985), no. 2, 185-195.  https://doi.org/10.1307/mmj/1029003185
  11. S. S. Miller and P. T. Mocanu, Differential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000. 
  12. V. Ravichandran and S. S. Kumar, Argument estimate for starlike functions of reciprocal order, Southeast Asian Bull. Math. 35 (2011), no. 5, 837-843. 
  13. B. A. Uralegaddi, M. D. Ganigi, and S. M. Sarangi, Univalent functions with positive coefficients, Tamkang J. Math. 25 (1994), no. 3, 225-230. https://doi.org/10.5556/j.tkjm.25.1994.4448