DOI QR코드

DOI QR Code

STUDY ON UNIFORMLY CONVEX AND UNIFORMLY STARLIKE MULTIVALENT FUNCTIONS ASSOCIATED WITH LIBERA INTEGRAL OPERATOR

  • Mayyadah Gh. Ahmed (The General Directorate of Education in Nineveh Governorate, School of Mathematical Sciences, University Sains Malaysia) ;
  • Shamani Supramaniam (School of Mathematical Sciences, University Sains Malaysia)
  • 투고 : 2022.01.13
  • 심사 : 2022.05.23
  • 발행 : 2023.03.03

초록

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ Ap using this operator.

키워드

참고문헌

  1. O.P. Ahuja, Integral operators of certain univalent functions, Int. J. Math. Soc., 8 (1985), 653-662. https://doi.org/10.1155/S0161171285000710
  2. H.F. Al-Janaby and M.Z. Ahmad, Differential inequalities related to Salagean type integral operator involving extended generalized Mittag-Leffler function, J. Phys. Conf. Ser., 1132(012061) (2019), 63-82. https://doi.org/10.1088/1742-6596/1132/1/012061
  3. H.F. Al-Janaby, F. Ghanim, and M. Darus, Some geometric properties of integral oerators proposed by Hurwitz-Lerch zeta function. IOP Conf. Ser. J. Phys. Conf. Ser., 1212(012010) (2019), 1-6. https://doi.org/10.1088/1742-6596/1212/1/012010
  4. M.K. Aouf, Some properties of Noor integral operator of (n+ p-1)-th order, Matematicki Vesnik, 61(4) (2009), 269-279.
  5. M.K. Aouf and T. Bulboaca, Subordination and superordination properties of multivalent functions defined by certain integral operators, J. Franklin Institute, 347 (2010), 641-653. https://doi.org/10.1016/j.jfranklin.2010.01.001
  6. S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), 429-446. https://doi.org/10.2307/1995025
  7. S.D. Bernardi, The radius of umvalence of certam analytic functions, Proc. Amer. Math. Soc., 24 (1970), 312-318. https://doi.org/10.1090/S0002-9939-1970-0251202-X
  8. S.S. Bhoosnurmath and S.R. Swamy,Rotaru starlike integral operators, Tamkang J. Math., 22(3), (1991), 291-297.
  9. T. Bulboaca, M.K. Aouf and R.M. El-Ashwah,Subordination properties of multivalent functions defined by certain integral operator, Banach J. Math. Anal., 6(2) (2012), 69-85. https://doi.org/10.15352/bjma/1342210161
  10. L. Cotirla A differential sandwich theorem for analytic functions defined by the integral operator, Studia Univ. "Babes-bolyai", Mathematica, 54(2) (2009), 13-21.
  11. F. Ghanim and Hiba F. Al-Janay, A certain subclass of univalent meromorphic functions defined by a linear operator associated with the Hurwitz-Lerch zeta function, Rad HAZU, Matematicke znanosti (Rad Hrvat. Akad. Znan. Umjet. Mat. Znan.), 23 (2019), 71-83.
  12. F. Ghanim and H.F. Al-Janaby, An analytical study on Mittag-Leffler-confluent hypergeometric functions with fractional integral operator. Math. Meth. Appl. Sci., 2020 (2020), 1-10, doi:10.1002/mma.6966.
  13. F. Ghanim, H.F. Al-Janaby and O. Bazighifan, Geometric properties of the meromorphic functions class through special functions associated with a linear operator. Adv Cont. Discr. Mod., 2022(17) (2022), https://doi.org/10.1186/s13662-022-03691-y.
  14. A.W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56 (1991), 87-92. https://doi.org/10.4064/ap-56-1-87-92
  15. A.W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl., 155 (1991), 364-370. https://doi.org/10.1016/0022-247x(91)90006-l
  16. I.B. Jung, Y.C. Kim, H. M. Srivastava,The Hardy space of analytic functions associated with certain oneparameter families of integral operators, J. Math. Anal. Appl., 176 (1993), 138-147. https://doi.org/10.1006/jmaa.1993.1204
  17. V. Kumar and S.L. Shukla,Jakubowski starlike integral operators, J. Austra. Math. Soc., 37 (1984), 117-127. https://doi.org/10.1017/S1446788700021807
  18. R.J. Libera , Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16 (1965), 755-758. https://doi.org/10.1090/S0002-9939-1965-0178131-2
  19. S.S. Miller and P.T. Mocanu, Libera transform of functions with bounded turning, J. Math. Anal. Appl., 276 (2002), 90-97. https://doi.org/10.1016/S0022-247X(02)00371-2
  20. K.I. Noor and M.A. Noor, On integral operators, J. Math. Anal. Appl., 238 (1999), 341-352. https://doi.org/10.1006/jmaa.1999.6501
  21. Gh. Oros and G.I. Oros, Convexity condition for the Libera integral operator, Complex Variables and Elliptic Equ., 51(1) (2006), 69-756. https://doi.org/10.1080/02781070500302520
  22. G.I. Oros, New differential subordinations obtained by using a differential-integral Ruscheweyh-Libera operator, Miskolc Math. Notes, 21(1) (2020), 303-317. https://doi.org/10.18514/mmn.2020.3084
  23. G.I. Oros, Study on new integral operators defined using confluent hypergeometric function, Advances in Diff. Equ., 2021(342) (2021), https://doi.org/10.1186/s13662-021-03497-4.
  24. F. Rønning, Integral representations for bounded starlike functions, Ann. Polon. Math., 60 (1995), 289-297. https://doi.org/10.4064/ap-60-3-289-297
  25. F. Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118 (1993), 189-196. https://doi.org/10.1090/S0002-9939-1993-1128729-7
  26. J. Sokol, Starlikeness of the Libera transform of functions with bounded turning, Appl. Math. Comput., 203 (2008), 273-276. https://doi.org/10.1016/j.amc.2008.04.036
  27. K.G. Subramanian, G. Murugusundaramoorthy, P. Balasubrahmanyam and H. Silverman, Subclasses of uniformly convex and uniformly starlike functions, Math. Japonica, 42(3) (1995), 517-522.
  28. K.G. Subramanian, T. Sudharsan, P. Balasubrahmanyam and H. Silverman , Classes of uniformly starlike functions, Publ. Math. Debrecen, 53(3-4) (1998), 309-315. https://doi.org/10.5486/PMD.1998.1946
  29. S.R. Swamy, Some subordination properties of multivalent functions defined by certain integral operators, J. Math. Comput. Sci., 3(2) (2013), 554-568.