Kyungpook Mathematical Journal

  • 제50권4호
  • /
  • Pages.499-507
  • /
  • 2010
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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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Univalent Holomorphic Functions with Negative and Fixed Finitely Many Coefficients in terms of Generalized Fractional Derivative

  • Ebadian, Ali (Department of mathematics, Faculty of Sciences, Urmia university) ;
  • Aghalary, Rasoul (Department of mathematics, Faculty of Sciences, Urmia university) ;
  • Najafzadeh, Shahram (Department of mathematics, University of Maragheh)
  • 투고 : 2009.04.12
  • 심사 : 2010.09.27
  • 발행 : 2010.12.31
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초록

A new class of univalent holomorphic functions with fixed finitely many coefficients based on Generalized fractional derivative are introduced. Also some important properties of this class such as coefficient bounds, convex combination, extreme points, Radii of starlikeness and convexity are investigated.

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참고문헌

  1. P. K. Beverji, L. Debnath and G. M. Shenan, Application of fractional derivative operators to the mapping properties of analytic functions, Fractional calculus and applied analysis, 5(2)(2002), 169-180.
  2. M. Darus and S. B. Joshi, On a subclass of analytic functions involving operators of farctional calculus, J. Rajastan Acad. Phy. Sci., 4(2)(2005), 73-84.
  3. A. Ebadian, S. Shams and Sh. Najafzadeh, Certain inequalities for p-valent meromorphic functions with alternating coefficients based on integral operator, AJMAA, 5(1)(2008), 1-5. https://doi.org/10.1080/14484846.2008.11464529
  4. V. P. Gupta, P. K. Jain, Certain classes of univalent functions with negative coefficients II, Bull. Austral. Math. Soc., 15(1976), 467-473. https://doi.org/10.1017/S0004972700022917
  5. Y. C. Kim, Y. S. Park and H. M. srivastava, A class of inclusion theorems associated with some functional integral operators, Proc. Acad., 67(9)(1991), Ser.A. https://doi.org/10.3792/pjaa.67.313
  6. Y. C. Kim and J. H. Choi, Integral means of the fractional derivative of univalent functions with negative coefficients, Mathematica Japonica, 51(2000), 453-457.
  7. S. Owa, On the distortion theorems. I, Kyungpook Math. J., 18(1978), 53-59.
  8. S. Owa and M. K. Aouf, On subclasses of univalent functions with negative coefficients, Pure Appl. Math. Sci. 29(1-2)(1989), 131-139.
  9. 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
  10. H. M. Srivastava, M. Saigo and S. Owa, A class of distortion theorems involving certain operators of fractional calculus, J. Math. Appl., 131, (1988), 412-420.
  11. H. M. Srivastava and S. Owa (Editors), Univalent functions, Fractional Calculus, and their Applications, Halsted Press (Elliss Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane, and Toronto, 1989.