Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators

Integral Transforms and Special Functions

Volumn 18, Issue 9, 2007, Pages 639-651

  Prajapat, J K ^a   Raina, R K ^b   Srivastava, H M ^c  

^a Sobhasaria Engineering College Sikar   (India)

^b University of Victoria ^*  (India)

^c UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Analytic functions; Close to convex functions; Convex functions; Fractional integral operators; Gauss hypergeometric function; Inclusion properties; Starlike functions; Strongly convex functions; Strongly starlike functions

Indexed keywords

EID: 35648951786     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652460701449668     Document Type: Article

References (15)

1. Srivastava, H.M. and Owa, S., (Eds), 1989, Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press (Chichester: Ellis Horwood Limited) (New York, Chichester, Brisbane and Toronto: John Wiley and Sons).
2. Srivastava, H.M. and Owa, S., 1992, Current Topics in Analytic Function Theory (Singapore, New Jersey, London and Hong kong: World Scientific Publishing Company).
3. Patel, J. and Cho, N.E., 2002, Argument estimates of analytic functions involving a linear operator. Mathematical Sciences Research Journal, 6(4), 190-203.
4. Srivastava, H.M., Saigo, M. and Owa, S., 1988, A class of distortion theorems involving certain operators of fractional calculus. Journal of Mathematical Analysis and Application, 131, 412-420.
5. Raina, R.K. and Srivastava, H.M., 1996, A certain subclass of analytic functions associated with operators of fractional calculus. Computers and Mathematics with Application, 32(7), 13-19.
6. Owa, S., 1978, On the distortion theorems. I. Kyungpook Mathematical Journal, 18, 53-59.
7. Srivastava, H.M. and Mishra, A.K., 2000, Applications of fractional calculus to parabolic starlike and uniformly convex functions. Computers and Mathematics Applications, 39(3-4), 57-69.
8. Jung, I.B., Kim, Y.C. and Srivastava, H.M., 1993, The Hardy space of analytic functions associated with certain one-parameter families of integral operators. Journal of Mathematical Analysis and Applications, 176, 138-147.
9. Gao, C.-Y., Yuan, S.-M. and Srivastava, H.M., 2005, Some functional inequalities and inclusion relationships associated with certain families of integral operators. Computers and Mathematics with Application, 49, 1787-1795.
10. Li, J.-L. and Srivastava, H.M., 1999, Some inclusion properties of the class. Integral Transforms and Special Functions, 8, 57-64.
11. Shanmugam, T.N., Sivasubramanian, S. and Srivastava, H.M., 2006, Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations. Integral Transforms and Special Functions, 17, 889-899.
12. Dziok, J., 2004, Applications of the Jack lemma. Acta Mathematica Hungarica, 105, 93-102.
13. Jahangiri, J.M., Kim, Y.C. and Srivastava, H.M., 2003, Construction of a certain class of harmonic close-to-convex functions associated with the Alexander integral transform.. Integral Transforms and Special Functions, 14, 237-242.
14. Nunokawa, M., 1992, On properties of non-Carathéodory functions. Proceedings of the Japan Academy Series A: Mathematical Sciences, 68, 152-153.
15. Liu, J.-L., 2002, Certain integral operator and strongly starlike functions. International Journal of Mathematics and Mathematical Sciences, 30, 569-574.