Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SUBORDINATIONS BY CERTAIN UNIVALENT FUNCTIONS ASSOCIATED WITH A FAMILY OF LINEAR OPERATORS

  • SEON HYE AN (Department of Applied Mathematics, College of Natural Sciences, Pukyong National University) ;
  • G. MURUGUSUNDARAMOORTHY (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • NAK EUN CHO (Department of Applied Mathematics, College of Natural Sciences, Pukyong National University)
  • Received : 2023.04.17
  • Accepted : 2023.09.12
  • Published : 2023.09.30
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Abstract

The aim of the present paper is to obtain some mapping properties of subordinations by certain univalent functions in the open unit disk associated with a family of linear operators. Moreover, we also consider some applications for integral operators.

Keywords

Acknowledgement

The third-named author was supported by the Basic Science Research Program through the National Research Foundation of the Republic of Korea (NRF) funded by the Ministry of Education, Science and Technology(Grant No. 2019R1I1A3A01050861).

References

  1. S.H. An, R. Srivastava and N.E. Cho, New approaches for subordination and superordination of multivalent functions associated with a family of linear operators, Accepted in Miskolc Math. Notes.
  2. S.D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2
  3. T. Bulboac˘a, Integral operators that preserve the subordination, Bull. Korean Math. Soc. 32 (1997), 627-636.
  4. T. Bulboac˘a, Subordination by alpha-convex functions, Kodai Math. J. 26 (2003), 267-278.
  5. T. Bulboac˘a, Generalization of a class of nonlinear averaging integral operators, Math. Nachr. 278 (2005), 34-42. https://doi.org/10.1002/mana.200310224
  6. N.E. Cho, Sushil Kumar, V. Kumar and V. Ravichandran, Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate, Turkish. J. Math. 42 (2018), 1380-1399.
  7. N.E. Cho, Sushil Kumar, V. Kumar and V. Ravichandran, Starlike functions related to the Bell numbers, Symmetry 11 (2019), Article No. 219.
  8. B.C. Carlson and D.B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 159 (1984), 737-745. https://doi.org/10.1137/0515057
  9. R.M. Goel and N.S. Sohi, A new criterion for p-valent functions, Proc. Amer. Math. Soc. 78 (1980), 353-357. https://doi.org/10.1090/S0002-9939-1980-0553375-4
  10. H. O. Guney, D. Breaz and S. Owa, Some Properties for Subordinations of Analytic Functions, Axioms 12 (2023), Article No. 131.
  11. D.J. Hallenbeck and T.H. MacGregor, Linear problems and convexity techniques in geometric function theory, Pitman Publishing Limited, London, 1984.
  12. S.S. Kumar, V. Kumar and V. Ravichandran, Subordination and superordination for multivalent functions defined by linear operators, Tamsui Oxf. J. Inf. Math. Sci. 29 (2013), 361-387.
  13. 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
  14. S.S. Miller and P.T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157-172.
  15. S.S. Miller, P.T. Mocanu and M.O. Reade, Subordination-preserving integral operators, Trans. Amer. Math. Soc. 283 (1984), 605-615. https://doi.org/10.1090/S0002-9947-1984-0737887-4
  16. S.S. Miller and P.T. Mocanu, Differential Subordination, Theory and Application, Marcel Dekker, Inc., New York, Basel, 2000.
  17. H. Naraghi, P. Najmadi and B. Taherkhani, New subclass of analytic functions defined by subordination, Internat. J. Nonlin. Anal. Appl. 12 (2021), 847-55.
  18. S. Owa and H.M. Srivastava, Some subordination theorems involving a certain family of integral operators, Integral Transforms Spec. Funct. 15 (2004), 445-454. https://doi.org/10.1080/10652460410001727563
  19. S. Owa and H.M. Srivastava, Some applications of the generalized Libera integral operator, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986), 125-128.
  20. G.I. Oros, G. Oros and S. Owa, Subordination properties of certain operators concerning fractional integral and Libera integral operator, Fractal Fract. 7 (2023), Article No. 42.
  21. Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Gottingen, 1975.
  22. S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115. https://doi.org/10.1090/S0002-9939-1975-0367176-1
  23. H. Saitoh, A linear operator and its applications of first order differential subordinations, Math. Japon. 44 (1996), 31-38.
  24. H.M. Srivastava and S. Owa, Some characterizations and distortions theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions, Nagoya Math. J. 106 (1987), 1-28. https://doi.org/10.1017/S0027763000000854