Kyungpook Mathematical Journal

  • 제55권2호
  • /
  • Pages.383-394
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  • 2015
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Certain Subclasses of k-Uniformly Starlike and Convex Functions of Order α and Type β with Varying Argument Coefficients

  • 투고 : 2013.06.15
  • 심사 : 2013.11.01
  • 발행 : 2015.06.23
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초록

In this paper, we define two new subclass of k-uniformly starlike and convex functions of order ${\alpha}$ type ${\beta}$ with varying argument of coefficients. Further, we obtain coefficient estimates, extreme points, growth and distortion bounds, radii of starlikeness, convexity and results on modified Hadamard products.

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참고문헌

  1. O. Altintas and S. Owa, On subclasses of univalent functions with negative coefficients, Pusan Kyongnam Math. J., 4(1988), 41-56.
  2. R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 28(1)(1997), 17-32.
  3. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14(1)(2003), 7-18. https://doi.org/10.1080/10652460304543
  4. J. Dziok and H. M. Srivastava, A unified class of analytic functions with varying argument of coefficients, Eur. J. Pure Appl. Math., 2(3)(2009), 302-324.
  5. R. M. El-Ashwah, M. K. Aouf, A. A. M. Hassan and A. H. Hassan, Certain new classes of analytic functions with varying arguments, J. Complex Anal., 2013, Art. ID 958210, 5 pp.
  6. A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1)(1991), 87-92.
  7. A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl., 155(2)(1991), 364-370. https://doi.org/10.1016/0022-247X(91)90006-L
  8. S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform. Spec. Funct., 9(2)(2000), 121-132. https://doi.org/10.1080/10652460008819249
  9. S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105(1-2)(1999), 327-336. https://doi.org/10.1016/S0377-0427(99)00018-7
  10. S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45(4)(2000), 647-657.
  11. N. Magesh, Certain subclasses of uniformly convex functions of order ${\alpha}$ and type ${\beta}$ with varying arguments, J. Egyptian Math. Soc., 21(3)(2013), 184-189. https://doi.org/10.1016/j.joems.2013.02.005
  12. W. C. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(2)(1992), 165-175.
  13. G. Murugusundaramoorthy and N. Magesh, On certain subclasses of analytic functions associated with hypergeometric functions, Appl. Math. Lett., 24(4)(2011), 494-500. https://doi.org/10.1016/j.aml.2010.10.048
  14. F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1)(1993), 189-196. https://doi.org/10.1090/S0002-9939-1993-1128729-7
  15. S. Shams, S. R. Kulkarni and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci., 53-56(2004), 2959-2961.
  16. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116. https://doi.org/10.1090/S0002-9939-1975-0369678-0
  17. H. Silverman, Univalent functions with varying arguments, Houston J. Math., 7(2)(1981), 283-287.
  18. Y. J. Sim, O. S. Kwon, N. E. Cho and H. M. Srivastava, Some classes of analytic functions associated with conic regions, Taiwanese J. Math., 16(1)(2012), 387-408.
  19. K. G. Subramanian, T. V. Sudharsan, P. Balasubrahmanyam and H. Silverman, Classes of uniformly starlike functions, Publ. Math. Debrecen, 53(3-4)(1998), 309-315.