DOI QR코드

DOI QR Code

ARGUMENT ESTIMATES FOR CERTAIN ANALYTIC FUNCTIONS IN A SECTOR

  • KIM, IN HWA (Department of Economics and International Business, Sam Houston State University) ;
  • CHO, NAK EUN (Department of Applied Mathematics, College of Natural Sciences, Pukyong National University)
  • Received : 2021.08.20
  • Accepted : 2021.12.07
  • Published : 2022.01.30

Abstract

The purpose of the present paper is to obtain some conditions for strongly starlikeness and univalence of normalized analytic functions in the open unit disk. Further, we prove an univalence and argument properties for certain integral operators.

Keywords

Acknowledgement

This work was supported by a Research Grant of Pukyong National University(2021).

References

  1. M.F. Ali and A. Vasudevarao, Logarithmic coefficients of some close-to-convex functions, Bull. Aust. Math. Soc. 95 (2017), 228-237. https://doi.org/10.1017/S0004972716000897
  2. D.A. Brannan and W.E. Kirwan, On some classes of bounded univalent functions, J. Lond. Math. Soc. 1 (1969), 431-443. https://doi.org/10.1112/jlms/s1-36.1.431
  3. A. Gangadharan and V. Ravichandran, Radii of convexity and strong starlikeness for some classes of analytic functions, J. Math. Anal. Appl. 211 (1997), 303-313.
  4. W. Janowski, Some extremal problems for certain families of analytic functions, I, Ann. Polon. Math. 28 (1973), 297-326. https://doi.org/10.4064/ap-28-3-297-326
  5. P.T. Mocanu, Alpha-convex integral operator and strongly starlike function, Studia Univ. Babes-Bolyai Math. 34 (1989), 18-24.
  6. M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A 69 (1993), 234-237. https://doi.org/10.3792/pjaa.69.234
  7. M. Nunokawa and D.K. Thomas, On convex and starlike functions in a sector, J. Aust. Math. Soc. Ser. A 60 (1996), 363-368. https://doi.org/10.1017/S1446788700037873
  8. M. Nunokawa, S. Owa, H. Saitoh, A. Ikeda, and N. Koike, Some results for strongly starlike functions, J. Math. Anal. Appl. 212 (1997), 98-106. https://doi.org/10.1006/jmaa.1997.5468
  9. M. Nunokawa, J. Soko'l and K. Trabka-Wieclaw, On the order of strongly starlikeness in some classes of starlike functions, Acta Math. Hung. 145 (2015), 142-149. https://doi.org/10.1007/s10474-014-0467-4
  10. M. Obradoric' and S. Owa, Some sufficient conditions for strongly starlikeness, Int. J. Math. Math. Sci. 24 (2000), 643-647. https://doi.org/10.1155/S0161171200004154
  11. S. Owa, H.M. Srivastava, T. Hayami and K. Kuroki, A new general idea for starlike and convex functions, Tamkang J. Math. 47 (2016), 445-454. https://doi.org/10.5556/j.tkjm.47.2016.2157
  12. J.H. Park, H.M. Srivastava, and N.E. Cho, Univalence and convexity conditions for certain integral operatorsassociated with the Lommel function of the first kind, AIMS Mathematics 6 (2021), 11380-11402. https://doi.org/10.3934/math.2021660
  13. Ch. Pommerenke, Univalent functions, Vandenhoeck and Ruprecht, 1975.
  14. H. Shiraishi, S. Owa and H.M. Srivastava, Sufficient conditions for strongly Caratheodory functions, Comput. Math. Appl. 62 (2011), 2978-2987. https://doi.org/10.1016/j.camwa.2011.08.004
  15. H. Silverman and E.M. Silvia, Sudclasses of starlike functions subordinate to convex functions, Can. J. Math. 37 (1985), 48-61. https://doi.org/10.4153/CJM-1985-004-7
  16. H.M. Srivastava and S. Owa, Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1989.
  17. H.M. Srivastava, Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A: Sci. 44 (2020), 327-344. https://doi.org/10.1007/s40995-019-00815-0
  18. H.M. Srivastava, R. Jan, A. Jan, W. Deebai and M. Shutaywi, Fractional-calculus analysis of the transmission dynamics of the dengue infection, Chaos 31 (2021), 1-18.