Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

SUBORDINATION AND SUPERORDINATION IMPLICATIONS ASSOCIATED WITH A CLASS OF NONLINEAR INTEGRAL OPERATORS

  • SEON HYE AN (Department of Applied Mathematics, College of Natural Sciences, Pukyong National University) ;
  • NAK EUN CHO (Department of Applied Mathematics, College of Natural Sciences, Pukyong National University)
  • Received : 2023.05.11
  • Accepted : 2023.06.26
  • Published : 2023.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

In the present paper, we investigate the subordination and superordination implications for a class of certain nonlinear integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Further, we extend some results given earlier as special cases of the main results presented here.

Keywords

Acknowledgement

This work was supported by a Research Grant of Pukyong National University(2023).

References

  1. M.K. Aouf, T. Bulboaca and T.M. Seoudy, Certain family of integral operators preserving subordination and superordination, Acta Math. Sci. Ser. B (Engl. Ed.) 34 (2014), 1166-1178. 
  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. Bulboaca, Integral operators that preserve the subordination, Bull. Korean Math. Soc. 34 (1997), 627-636. 
  4. T. Bulboaca, A class of superordination-preserving integral operators, Indag. Math. N. S. 13 (2002), 301-311.  https://doi.org/10.1016/S0019-3577(02)80013-1
  5. T. Bulboaca, Differential subordination and superordination-preserving integral operators, Trans. Inst. Math. Nat. Acad. Sci. Ukraine 3 (2004), 19-28. 
  6. T. Bulboaca, Sandwich-type theorems for a class of integral operators, Bull. Belg. Math. Soc. Simon Stevin 13 (2006), 537-550.  https://doi.org/10.36045/bbms/1161350695
  7. T. Bulboaca, Sandwich-type results for a class of convex integral operators, Acta Math. Sci. Ser. B Engl. Ed. 32 (2012), 989-1001.  https://doi.org/10.1016/S0252-9602(12)60074-5
  8. N.E. Cho and T. Bulboaca, Subordination and superordination properties for a class of integral operators, Acta Math. Sin. (Engl. Ser.) 26 (2010), 515-522.  https://doi.org/10.1007/s10114-010-8488-6
  9. N.E. Cho, T. Bulboaca and H.M. Srivastava, A general family of integral operators and associated subordination and superordination properties of some special analytic function classes, Appl. Math. Comput. 219 (2012), 2278-2288. 
  10. N.E. Cho, H.M. Srivastava, A class of nonlinear integral operators preserving subordination and superordination, Integral Transforms Spec. Funct. 18 (2007), 95-107.  https://doi.org/10.1080/10652460601135342
  11. D.J. Hallenbeck and T.H. MacGregor, Linear problems and convexity techniques in geometric function theory, Pitman Publishing Limited, London, 1984. 
  12. W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 2 (1952), 169-185. 
  13. V. Kumar and S.L. Shukla, Jakubowski starlike integral operators, J. Austral. Math. Soc. (Series A) 37 (1984), 117-127.  https://doi.org/10.1017/S1446788700021807
  14. 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
  15. S.S. Miller and P.T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), 157-171. 
  16. S.S. Miller and P.T. Mocanu, Univalent solutions of Briot-Bouquet differential equations, J. Different. Equations 567 (1985), 297-309.  https://doi.org/10.1016/0022-0396(85)90082-8
  17. S.S. Miller and P.T. Mocanu, Classes of univalent integral operators, J. Math. Anal. Appl. 157 (1991), 147-165.  https://doi.org/10.1016/0022-247X(91)90141-L
  18. S.S. Miller and P.T. Mocanu, Differential Subordinations, Theory and Applications, Marcel Dekker, Inc., New York, Basel, 2000. 
  19. S.S. Miller and P.T. Mocanu, Subordinants of differential superordinations, Complex Var. Theory Appl. 48 (2003), 815-826. 
  20. S.S. Miller, P.T. Mocanu and M.O. Reade, Starlike integral operators, Pacific J. Math. 79 (1978), 157-168.  https://doi.org/10.2140/pjm.1978.79.157
  21. 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
  22. S. Owa, 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
  23. Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Gottingen, 1975. 
  24. H.M. Srivastava and M.K. Aouf, A.O. Mostafa and H.M. Zayed, Certain subordination-preserving family of integral operators associated with p-valent functions, Appl. Math. Inf. Sci. 11 (2017), 951-960. https://doi.org/10.18576/amis/110401