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Distortion and convolutional theorems for operators of generalized fractional calculus involving wright function

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Języki publikacji
EN
Abstrakty
EN
Using the Wright's generalized hypergeornetric function, we investigate a class W(q,s: A, B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W(q,s: A, B, λ) . Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeornetric) operators of fractional calculus.
Wydawca
Rocznik
Strony
183--192
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
autor
Bibliografia
  • [1] Aouf, M. K., Dziok, J., Certain class of analytic Junctions associated with the Wright generalized hypergeometric function, ,J. Math. Appl. 30 (2008), 23-32.
  • [2] Dziok, J., Raina, R. K., Families of analytic functions associated with the Wright generalized hypergeometric function, Demonstratio Math. 37(3) (2004), 533-542.
  • [3] Dziok, J., Raina, R. K., Srivastava, II. M., Some classes of analytic functions associated with, operators on Hilbert. space involving Wright's generalized hypergeometric function, Proc. Jangieon Math. Soc. 7 (2004), 43-55.
  • [4] Dziok, J., Srivastava, H. M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003), 7-18.
  • [5] Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), 1-13.
  • [6] Kiryakova, V., Generalized Fractional Calculus and Applications, Longman & J. Wiley, Harlow-New York, 1994.
  • [7] Kiryakova, V., Saigo, M., Criteria for generalized fractional integrals to preserve univalency of analytic functions, C. R. Acad. Bulgare Sci. 58(10) (2005), 1127-1134.
  • [8] Kiryakova, V., Saigo, M., Owa, S. Distortion and characterization theorems for generalized fractional integration operators involving H-function in subclasses of univalent functions, Fukuoka Univ. Sci. Rep. 34(1) (2004), 1-16.
  • [9] Kiryakova. V., Saigo, M., Srivastava, H. M., Some criteria for univalence of analytic functions involving generalized fractional calculus operators, Fract. Calc. Appl. Anal. 1(1) (1998), 79-104.
  • [10] Owa, S., On the distortion theorems. I, Kyungpook Math. J. 18 (1978), 53-59.
  • [11] Patel, J., Acharya, M., Certain subclasses of starlike. functions with negative coefficients. Bull. Calcuta Math. Soc. 87 (1995), 265-276.
  • [12] Prudnikov, A. P., Brychkov, Yu. A., Marichev, O. I., Integrals and Series. Vol. 3: More Special Functions, Gordon & Breach Sci. Publ., New York, 1990.
  • [13] Raina, R. K., Kalia, R. N., Characterizations for subclasses of analytic functions connecting linear fractional calculus operators, Fract. Calc. Appl. Anal. 1(4) (1998). 335-350.
  • [14] Raina, R. K., Nahar, T. S., A note on boundedness properties of Wright's generalized hypergeometric function, Ann. Math. Blaise Pascal 4 (1997), 83-95.
  • [15] Raina, R. K., Nahar, T. S., On characterization of certain Wright's generalized hypergeometric functions involving certain subclasses of analytic functions. Informatica (Vilnius) 10 (1999), 219-230.
  • [16] Raina, R. K., Nahar, T. S., On uniwalent and starlike Wright's hypergeometric functions, Rend. Sem. Mat. Univ. Padova 95 (1996), 11-22.
  • [17] Saigo, M., A certain boundary value problem for the Euler-Darboux equation, Math. Japon. 24 (1980), 377-385.
  • [18] Saigo, M., A remark on integral operators involving the Gauss hypergeornetric functions, Math. Rep. Kyushu Univ. 11 (1978), 135-143.
  • [19] Srivastava, H. M., Gupta, C. K., Goyal, S. P., The H-Functions of One and. Two Variables with Applications, South Asian Publ., New Delhi, 1982.
  • [20] Srivastava, H. M., Owa, S., An application of the fractional derivative. Math. Japon. 29 (1984), 383-389.
  • [21] Srivastava, H. M., Owa, S., (editors). Current Topics in Analytic Function Theory. World Sci. Publ. Comp., Singapore-New Jersey-London-Hong Kong, 1992.
  • [22] Srivastava, H. M.. Saigo, M., Owa, S., A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl. 131 (1988), 412-420.
  • [23] Wright, E. M., The asymptotic expansion of the generalized hypergeometric function. Proc. London Math. Soc. (3) 46 (1946), 389-408.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0006-0022
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