Applications of generalized fractional integral operator to unified subclass of prestarlike functions with negative coefficients

Santosh B. Joshi, Sayali S. Joshi, Haridas Pawar

Abstract


In this paper we have introduced and studied various properties of unified class of prestarlike functions with negative coefficients in the unit disc U.Also distortion theorem involving a generalized fractional integral operator for functions in this class are established.

Keywords


coefficient estimates, univalent function,distortion theorem

Full Text:

PDF

References


S.B. Joshi, On subclasses of prestarlike functions with negative coecients, Studia Univ. Babes-Bolyai Matematica, LIV(2), (2009), 65-74.

V.S. Kiryakova, Generalized fractional calculus and applications, Pitman Re-search Notes in Math., Longman Publishers, London, (1993).

V.S. Kiryakova, H. M. Srivastava, Generalized multiple Riemann-Liouville fractional dierintegrals and applications in univalent function theory, Analysis Geometry and Groups: A Riemann Legacy Volume, Hadronic Press, Palm Harbor, Florida, U.S.A., (1993), 191-226.

S. Owa, B.A. Uralegaddi, A class of functions prestarlike of order , Bull. Korean Math. Soc., 21, (1984), 77-85.

R. K. Raina, M. Bolia, On certain classes of distortion theorems involving generalized fractional integral operators, Bull. Inst. Math. Acad. Sinica, 26(4), (1998), 301-307.

R. K. Raina, M. Saigo, A note on fractional calculus operators involving Fox's H-function on space Fp; and F0 p;, Recent advances in fractional calculus, (1993), 219-229.

R. K. Raina, H. M. Srivastava, A unied presentation of certain subclasses of prestarlike functions with negative coecients, Int. J. Comp. Math. Appl.,38, (1999), 71-78.

T. Sheil-Small, H. Silverman, E. M. Silvia,Convolutions multipliers and starlike functions, J. Anal. Math., 41, (1982), 181-192.

H.Silverman, Univalent functions with negative coecients, Proc. Amer. Math. Soc., 51, (1975), 109-116.

H. M. Srivastava, M. K. Aouf, Some applications of fractional calculus operators to certain subclasses of prestarlike functions with negative coecients, Comp. Math. Appl., 30(1), (1995), 53-61.

H. M. Srivastava, S. Owa(Editors), Univalent functions, Fractional calculus and their applications, Halsted Press, John Wiley and Sons, New York, (1989).




DOI: http://dx.doi.org/10.24193/subbmath.2018.1.04

Refbacks

  • There are currently no refbacks.