Journal of applied mathematics & informatics

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

DOI QR Code

NORMALIZED DINI FUNCTIONS CONNECTED WITH k-UNIFORMLY CONVEX AND k-STARLIKE FUNCTIONS

  • ECE, SADETTIN (Institute of Natural and Applied Science, Dicle University) ;
  • EKER, SEVTAP SUMER (Department of Mathematics, Faculty of Science, Dicle University) ;
  • SEKER, BILAL (Department of Mathematics, Faculty of Science, Dicle University)
  • Received : 2020.09.23
  • Accepted : 2020.12.27
  • Published : 2021.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.

Keywords

References

  1. R.M. Ali, S.K. Lee, and S.R. Mondal, Inequalities on an extended Bessel function, J. Inequal. Appl. 66 (2018), 1-22.
  2. R.M. Ali, S.K. Lee, and S.R. Mondal, Starlikeness of a generalized Bessel function, Bull. Belg. Math. Soc. Simon Stevin 25 (2018), 527-540.
  3. A. Baricz, Generalized Bessel functions of the first kind, Lecture Notes in Math. 1994, Springer-Verlag, Berlin, 2010.
  4. A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen 73 (2008), 155-178.
  5. A. Baricz, The radius of convexity of normalized Bessel functions of the first kind, Analysis and Applications 12 (2014), 485-509. https://doi.org/10.1142/S0219530514500316
  6. A. Baricz, E. Deniz, M. Caglar, H. Orhan, Differential subordinations involving generalized Bessel functions, Bull. Malays. Math. Sci. Soc. 38 (2015), 1255-1280. https://doi.org/10.1007/s40840-014-0079-8
  7. A. Baricz, P.A. Kupan, R. Szasz, The radius of starlikeness of normalized Bessel functions of the first kind, Proc. Amer. Math. Soc. 142 (2014), 2019-2025. https://doi.org/10.1090/S0002-9939-2014-11902-2
  8. A. Baricz, S. Ponnusamy, Differential inequalities and Bessel functions, J. Math. Anal. Appl. 400 (2013), 558-567. https://doi.org/10.1016/j.jmaa.2012.11.050
  9. A. Baricz, S. Ponnusamy, S. Singh, Modified Dini functions: monotonicity patterns and functional inequalities, Acta Math. Hungar. 149 (2016), 120-142. https://doi.org/10.1007/s10474-016-0599-9
  10. A. Baricz, R. Szasz, Close-to-Convexity of Some Special Functions and Their Derivatives, Bull. Malays. Math. Sci. Soc. 39 (2016), 427-437. https://doi.org/10.1007/s40840-015-0180-7
  11. A. Baricz, E. Deniz and N. Yagmur, Close-to-convexity of normalized Dini functions, Math. Nachr. 289 (2016), 1721-1726. https://doi.org/10.1002/mana.201500009
  12. D. Bernoulli, Demonstrationes theorematum suorum de oscillationibus corporum filo flexili connexorum et catenae verticaliter suspensae, Commentarii Academiae Scientiarum Imperialis Petropolitanae 7 (1734), 162-173.
  13. R.K. Brown, Univalence of Bessel functions, Proc. Amer. Math. Soc. 11 (1960), 278-283. https://doi.org/10.1090/S0002-9939-1960-0111846-6
  14. L. Galue, A generalized Bessel function, Integral Transforms Spec. Funct. 14 (2003), 395-401. https://doi.org/10.1080/1065246031000074362
  15. S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. and Math. 105 (1999), 327-336. https://doi.org/10.1016/S0377-0427(99)00018-7
  16. S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), 647-657.
  17. E. Kreyszig and J. Todd, The radius of univalence of Bessel functions , Illinois J. Math. 4 (1960), 143-149. https://doi.org/10.1215/ijm/1255455740
  18. F.W.J. Olver, D.W. Lozier, R.F. Boisvert, and C.W. Clark(eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge, 2010.
  19. R. Szasz and P.A. Kupan, About the univalence of the Bessel functions, Stud. Univ. Babes-Bolyai Math. 54 (2009), 127-132.
  20. N. Watson, A Treatise of the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1995.