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SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY LOMMEL OPERATOR

  • Received : 2021.04.29
  • Accepted : 2021.09.02
  • Published : 2022.04.30

Abstract

We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.

Keywords

References

  1. A. Baricz, D. K. Dimitrov, H. Orhan, and N. Yagmur, Radii of starlikeness of some special functions, Proc. Amer. Math. Soc. 144 (2016), no. 8, 3355-3367. https://doi.org/10.1090/proc/13120
  2. S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. https://doi.org/10.2307/1995025
  3. P. Eenigenburg, S. S. Miller, P. T. Mocanu, and M. O. Reade, On a Briot-Bouquet differential subordination, Rev. Roumaine Math. Pures Appl. 29 (1984), no. 7, 567-573.
  4. S. S. Miller and P. T. Mocanu, Differential subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000.
  5. B. Pinchuk, Functions of bounded boundary rotation, Israel J. Math. 10 (1971), 6-16. https://doi.org/10.1007/BF02771515
  6. St. Ruscheweyh and T. Sheil-Small, Hadamard products of Schlicht functions and the Polya-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135. https://doi.org/10.1007/BF02566116
  7. Y. J. Sim, O. S. Kwon, and N. E. Cho, Geometric properties of Lommel functions of the first kind, Symmetry 10 (2018), 445. https://doi.org/10.3390/sym10100445
  8. N. Yagmur, Hardy space of Lommel functions, Bull. Korean Math. Soc. 52 (2015), no. 3, 1035-1046. https://doi.org/10.4134/BKMS.2015.52.3.1035