Research ArticleOpen AccessGoogle Scholar indexed
Applications of Multivalent Functions Associated with Generalized Fractional Integral Operator
Department of Mathematics Education, Daegu National University of Education, Daegu, South Korea
- 1 Department of Mathematics Education, Daegu National University of Education, Daegu, South Korea
Advances in Pure Mathematics·Volume 03 (2013)·Pages 1–5·Published 11 January 2013·DOI10.4236/apm.2013.31001
Copy link · social · email
Abstract
By using a method based upon the Briot-Bouquet differential subordination, we investigate some subordination properties of the generalized fractional integral operator which was defined by Owa, Saigo and Srivastava [1]. Some interesting further consequences are also considered.
KeywordsMultivalent FunctionsSubordinationGaussian Hypergeometric FunctionFractional Integral Operator
- S. Owa, M. Saigo and H. M. Srivastava, “Some Characterization Theorems for Starlike and Convex Functions Involving a Certain Fractional Integral Operator,” Journal of Mathematical Analysis and Applications, Vol. 140, No. 2, 1989, pp. 419-426. doi:10.1016/0022-247X(89)90075-9
- S. G. Samko, A. A. Kilbas and O. I. Marichev, “Fractional Integral and Derivatives, Theory and Applications,” Gordon and Breach, New York, Philadelphia, London, Paris, Montreux, Toronto, Melbourne, 1993.
- H. M. Srivastava and R. G. Buschman, “Theory and Applications of Convolution Integral Equations,” Kluwer Academic Publishers, Dordrecht, Boston, London, 1992.
- M. Saigo, “A Remark on Integral Operators Involving the Gauss Hypergeometric Functions,” Mathematical Reports, Kyushu University, Vol. 11, No. 2, 1977-1978, pp. 135-143.
- J. H. Choi, “Note on Differential Subordination Associated with Fractional Integral Operator,” Far East Journal of Mathematical Sciences, Vol. 26, No. 2, 2007, pp. 499- 511.
- I. B. Jung, Y. C. Kim and H. M. srivastava, “The Hardy Space of Analytic Functions Associated with Certain One-Parameter Families of Integral Operators,” Journal of Mathematical Analysis and Applications, Vol. 176, No. 1, 1993, pp. 138-147. doi:10.1006/jmaa.1993.1204
- J.-L. Liu, “Notes on Jung-Kim-Srivastava Integral Operator,” Journal of Mathematical Analysis and Applications, Vol. 294, No. 1, 2004, pp. 96-103. doi:10.1016/j.jmaa.2004.01.040
- R. M. EL-Ashwash and M. K. Aouf, “Some Subclasses of Multivalent Functions Involving the Extended Fractional Differintegral Operator,” Journal of Mathematical Inequalities, Vol. 4, No. 1, 2010, pp. 77-93.
- J. Patel, A. K. Mishra and H. M. Srivastava, “Classes of Multinalent Analytic Functions Involving the Dziok-Srivastava Operator,” Computers and Mathematics with Applications, Vol. 54, No. 5, 2007, pp. 599-616. doi:10.1016/j.camwa.2006.08.041
- S. S. Miller and P. T. Mocanu, “Differential Subordinations and Univalent Functions,” Michigan Mathematical Journal, Vol. 28, No. 2, 1981, pp. 157-172. doi:10.1307/mmj/1029002507
- S. D. Bernardi, “Convex and Starlike Univalent Functions,” Transactions of the American Mathematical Society, Vol. 135, 1969, pp. 429-446. doi:10.1090/S0002-9947-1969-0232920-2
- R. J. Libera, “Some Classes of Regular Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 16, No. 4, 1965, pp. 755-758. doi:10.1090/S0002-9939-1965-0178131-2