Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON SHARP GENERAL COEFFICIENT ESTIMATES FOR 𝜗-SPIRALLIKE FUNCTIONS

  • Received : 2022.04.22
  • Accepted : 2022.06.28
  • Published : 2023.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper attempts to investigate a new subfamily 𝓢𝓣𝜗,𝜎 (𝛼, 𝛽, 𝛾, 𝜇) of spirallike functions endowed with Mittag-Leffler and Wright functions. The paper further investigates sharp coefficient bounds for functions that belong to this class.

Keywords

References

  1. O. Ahuja, S. Kumar, and A. Cetinkaya, Normalized multivalent functions connected with generalized Mittag-Leffler functions, Acta Univ. Apulensis Math. Inform. No. 67 (2021), 111-123. https://doi.org/10.17114/j.aua 
  2. D. Bansal and K. Mehrez, On a new class of functions related with Mittag-Leffler and Wright functions and their properties, Commun. Korean Math. Soc. 35 (2020), no. 4, 1123-1132. https://doi.org/10.4134/CKMS.c200022 
  3. G. A. Dorrego and R. A. Cerutti, The k-Mittag-Leffler function, Int. J. Contemp. Math. Sci. 7 (2012), no. 13-16, 705-716. 
  4. Lj. Gajic and B. Stankovic, Some properties of Wright's function, Publ. Inst. Math. (Beograd) (N.S.) 20(34) (1976), 91-98. 
  5. K. S. Gehlot, The p-k Mittag-Leffler function, Palest. J. Math. 7 (2018), no. 2, 628-632. 
  6. P. Humbert, Quelques resultats relatifs a la fonction de Mittag-Leffler, C. R. Acad. Sci. Paris 236 (1953), 1467-1468. 
  7. R. J. Libera, Univalent α-spiral functions, Canadian J. Math. 19 (1967), 449-456. https://doi.org/10.4153/CJM-1967-038-0 
  8. Y. Luchko, The Wright function and its applications, in Handbook of fractional calculus with applications. Vol. 1, 241-268, De Gruyter, Berlin, 2019. 
  9. F. Mainardi and A. Consiglio, The Wright functions of the second kind in Mathematical Physics, Mathematics 8 (2020), no. 6, 1-26.  https://doi.org/10.3390/math8060884
  10. N. Mustafa, Univalence of certain integral operators involving normalized Wright functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 (2017), no. 1, 19-28. https://doi.org/10.1501/Commua1_0000000771 
  11. J. K. Prajapat, Certain geometric properties of the Wright function, Integral Transforms Spec. Funct. 26 (2015), no. 3, 203-212. https://doi.org/10.1080/10652469.2014.983502 
  12. A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl. 336 (2007), no. 2, 797-811. https://doi.org/10.1016/j.jmaa.2007.03.018 
  13. L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pro Pestovani Matematiky a Fysiky 62 (1933), 12-19.  https://doi.org/10.21136/CPMF.1933.121951
  14. A. Wiman, Uber den Fundamentalsatz in der Teorie der Funktionen Ea(x), Acta Math. 29 (1905), no. 1, 191-201. https://doi.org/10.1007/BF02403202 
  15. E. M. Wright, On the Coefficients of Power Series Having Exponential Singularities, J. London Math. Soc. 8 (1933), no. 1, 71-79. https://doi.org/10.1112/jlms/s1-8.1.71