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On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator

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Abstract

The purpose of this paper is to introduce subclasses of multivalent functions by using linear operator defined by generalized fractional differintegral operator. We investigate various properties for functions of these subclasses.

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References

  1. Aouf, M.K., Seoudy, T.M.: Some properties of certain subclasses of \(p\)-valent Bazilevič functions associated with the generalized operator. Appl. Math. Lett. 24(11), 953–1958 (2011)

    Article  MATH  Google Scholar 

  2. Goyal, G.P., Prajapat, J.K.: A new class of analytic \(p\)-valent functions with negative coefficients and fractional calculus operators. Tamsui Oxford Univ. J. Math. Sci. 20(2), 175–186 (2004)

    MathSciNet  MATH  Google Scholar 

  3. Miller, S.S., Mocanu, P.T.: Second order differential inequalities in the complex plane. J. Math. Anal. Appl. 65(2), 289–305 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mostafa, A.O., Aouf, M.K., Shamandy, A., Adwan, E.A.: Certain subclasses of \(p\)-valent meromorphic functions associated with a new operator. J. Complex Anal. 1–4 (2013)

  5. Muhammad, A.: Some properties of the generalized class of non-Bazilevič functions. Acta Univ. Apulensis Math. Inform. 25, 307–312 (2011)

    Google Scholar 

  6. Noor, K.I.: On subclasses of close-to-convex functions of higher order. Int. J. Math. Math. Sci. 15, 279–290 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Noor, K.I., Muhammad, A.: On certain properties of the class of generalized \(p\)-valent non-Bazilevič functions. Acta Univ. Apulensis Math. Inform. 20, 25–30 (2009)

    MATH  Google Scholar 

  8. Obradović, M.: A class of univalent functions. Hokkaido Math. J. 27(2), 329–355 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Owa, S.: On the distortion theorems. I. Kyungpook Math. J. 18, 53–591 (1978)

    MathSciNet  MATH  Google Scholar 

  10. Owa, S.: On certain Bazilevi\(\check{c}\) functions of order \( \beta, \)Internat. J. Math. Math. Sci. 15(3), 613–616 (1992)

    Article  MathSciNet  Google Scholar 

  11. Owa, S., Srivastava, H.M.: Univalent and starlike generalized hypergeometric functions. Canad. J. Math. 39, 1057–1077 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  12. Padmanabhan, K.S., Parvatham, R.: Properties of a class of functions with bounded boundary rotation. Ann. Polon. Math. 31, 311–323 (1975)

    MathSciNet  MATH  Google Scholar 

  13. Pinchuk, B.: Functions with bounded boundary rotation. Israel J. Math. 10, 7–16 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  14. Prajapat, J.K., Aouf, M.K.: Majorization problem for certain class of \(p\)-valently analytic function defined by generalized fractional differintegral operator. Comput. Math. Appl. 63(1), 42–47 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Prajapat, J.K., Raina, R.K., Srivastava, H.M.: Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators. Integral Transforms Spec. Funct. 18(9), 639–651 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Seoudy, T.M., Aouf, M.K.: Subclasses of \(p-\)valent functions of bounded boundary rotation involving the generalized fractional differintegral operator. C. R. A. Cad. Sci. Paris, Ser. I 351, 787–792 (2013)

  17. Srivastava, H.M., Owa, S.: Some characterizations and distortions theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators and certain subclasses of analytic functions. Nagoya Math. J. 106, 1–28 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  18. Srivastava, H.M., Saigo, M., Owa, S.: A class of distortion theorems involving certain operators of fractional calculus. J. Math. Anal. Appl. 131, 412–420 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tang, H., Deng, G.-T., Li, S.-H., Aouf, M.K.: Inclusion results for certain subclasses of spiral-like multivalent functions involving a generalized fractional differintegral operator. Integral Transforms Spec. Funct. 24(11), 873–883 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, Z., Gao, C., Liao, M.: On certain generalized class of non-Bazilevič functions. Acta Math. Acad. Paedagog. Nyhazi (N.S.) 21, 147–154 (2005)

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    M. K. Aouf & A. O. Mostafa

  2. Department of Mathematics, Faculty of Science, Menofia University, Shebin Elkom, 32511, Egypt

    H. M. Zayed

Authors
  1. M. K. Aouf
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  2. A. O. Mostafa
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  3. H. M. Zayed
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Correspondence to H. M. Zayed.

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Aouf, M.K., Mostafa, A.O. & Zayed, H.M. On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator. Afr. Mat. 28, 99–107 (2017). https://doi.org/10.1007/s13370-016-0433-0

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  • DOI: https://doi.org/10.1007/s13370-016-0433-0

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