대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권2호
  • /
  • Pages.407-420
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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GEOMETRIC PROPERTIES OF STARLIKENESS INVOLVING HYPERBOLIC COSINE FUNCTION

  • Om P. Ahuja (Department of Mathematical Sciences Kent State University) ;
  • Asena Cetinkaya (Department of Mathematics and Computer Science Istanbul Kultur University) ;
  • Sushil Kumar (Bharati Vidyapeeth's College of Engineering)
  • 투고 : 2023.05.06
  • 심사 : 2024.01.25
  • 발행 : 2024.04.30
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초록

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

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참고문헌

  1. O. P. Ahuja, S. Kumar, and V. Ravichandran, Applications of first order differential subordination for functions with positive real part, Stud. Univ. Babes-Bolyai Math. 63 (2018), no. 3, 303-311. https://doi.org/10.24193/subbmath.2018.3.02
  2. A. Alotaibi, M. Arif, M. A. Alghamdi, and S. Hussain, Starlikness associated with cosine hyperbolic function, Mathematics 8 (2020), no. 7, 1118. https://doi.org/10.3390/math8071118
  3. K. O. Babalola, On H3(1) Hankel determinant for some classes of univalent functions, Ineq. Theory Appl. 6 (2010), 1-7.
  4. K. Bano and M. Raza, Starlike functions associated with cosine functions, Bull. Iranian Math. Soc. 47 (2021), no. 5, 1513-1532. https://doi.org/10.1007/s41980-020-00456-9
  5. N. Bohra, S. Kumar, and V. Ravichandran, Some special differential subordinations, Hacet. J. Math. Stat. 48 (2019), no. 4, 1017-1034. https://doi.org/10.15672/hjms.2018.570
  6. N. Bohra, S. Kumar, and V. Ravichandran, Applications of Briot-Bouquet differential subordination, J. Class. Anal. 18 (2021), no. 1, 17-28. https://doi.org/10.7153/jca-2021-18-02
  7. P. L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften, 259, Springer, New York, 1983.
  8. P. J. Eenigenburg, S. S. Miller, P. T. Mocanu, and M. O. Reade, On a Briot-Bouquet differential subordination, in General inequalities, 3 (Oberwolfach, 1981), 339-348, Internat. Schriftenreihe Numer. Math., 64, Birkhauser, Basel, 1983.
  9. R. M. Goel, On the partial sums of a class of univalent functions, Ann. Univ. Mariae Curie-Sk lodowska Sect. A 19 (1965), 17-23.
  10. D. J. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195. https://doi.org/10.2307/2040127
  11. K. Hu and Y. F. Pan, On a theorem of Szego, J. Math. Res. Exposition 4 (1984), no. 1, 41-44.
  12. B. Kowalczyk, A. Lecko, and Y. J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc. 97 (2018), no. 3, 435-445. https://doi.org/10.1017/S0004972717001125
  13. S. Kumar and A. Cetinkaya, Coefficient inequalities for certain starlike and convex functions, Hacet. J. Math. Stat. 51 (2022), no. 1, 156-171. https://doi.org/10.15672/hujms.778148
  14. V. Kumar, N. E. Cho, V. Ravichandran, and H. M. Srivastava, Sharp coefficient bounds for starlike functions associated with the Bell numbers, Math. Slovaca 69 (2019), no. 5, 1053-1064. https://doi.org/10.1515/ms-2017-0289
  15. S. Kumar and V. Ravichandran, Subordinations for functions with positive real part, Complex Anal. Oper. Theory 12 (2018), no. 5, 1179-1191. https://doi.org/10.1007/s11785-017-0690-4
  16. S. K. Lee, V. Ravichandran, and S. Supramaniam, Bounds for the second Hankel determinant of certain univalent functions, J. Inequal. Appl. 2013 (2013), 281, 17 pp. https://doi.org/10.1186/1029-242X-2013-281
  17. T. H. MacGregor, Majorization by univalent functions, Duke Math. J. 34 (1967), 95-102. http://projecteuclid.org/euclid.dmj/1077376845 1077376845
  18. S. S. Miller and P. T. Mocanu, Univalent solutions of Briot-Bouquet differential equations, J. Differential Equations 56 (1985), no. 3, 297-309. https://doi.org/10.1016/0022-0396(85)90082-8
  19. A. Naz, S. Kumar, and V. Ravichandran, Coefficient functionals and radius problems of certain starlike functions, Asian-Eur. J. Math. 15 (2022), no. 5, Paper No. 2250089, 19 pp. https://doi.org/10.1142/S1793557122500899
  20. M. Obradovic, N. Tuneski, and P. Zaprawa, Sharp bounds of the third Hankel determinant for classes of univalent functions with bounded turning, Math. Bohem. 147 (2022), no. 2, 211-220. https://doi.org/10.21136/MB.2021.0078-20
  21. C. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. London Math. Soc. 41 (1966), 111-122. https://doi.org/10.1112/jlms/s1-41.1.111
  22. B. Rath, K. Sanjay Kumar, D. V. Krishna, and A. Lecko, The sharp bound of the third Hankel determinant for starlike functions of order 1/2, Complex Anal. Oper. Theory 16 (2022), no. 5, Paper No. 65, 8 pp. https://doi.org/10.1007/s11785-022-01241-8
  23. V. Ravichandran, Geometric properties of partial sums of univalent function, Mathematics Newsletter 22 (2012), no. 3, 208-221.
  24. V. Ravichandran and S. Verma, Bound for the fifth coefficient of certain starlike functions, C. R. Math. Acad. Sci. Paris 353 (2015), no. 6, 505-510. https://doi.org/10.1016/j.crma.2015.03.003
  25. H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209 (1997), no. 1, 221-227. https://doi.org/10.1006/jmaa.1997.5361
  26. E. M. Silvia, On partial sums of convex functions of order α, Houston J. Math. 11 (1985), no. 3, 397-404.
  27. G. Szego, Zur Theorie der schlichten Abbildungen, Math. Ann. 100 (1928), no. 1, 188-211. https://doi.org/10.1007/BF01448843
  28. H. Tang, H. M. Srivastava, S. Li, and G. Deng, Majorization results for subclasses of starlike functions based on the sine and cosine functions, Bull. Iranian Math. Soc. 46 (2020), no. 2, 381-388. https://doi.org/10.1007/s41980-019-00262-y