Abstract
The purpose of the present paper is to investigate some subordination and other properties of several subclasses of multivalent functions which are defined by the Srivastava–Saigo–Owa fractional differintegral operator. Inclusion relations for functions in the class \(\mathcal {S}_{p,\lambda ,\mu ,\eta }^{m,\delta ,\zeta }(\alpha; A, B)\) and the images of these functions by the generalized Bernardi–Libera–Livingston integral operator are also considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Oboudi, F.M.: On univalent functions defined by a generalized Sălăgean operator. Int. J. Math. Math. Sci. 27, 1429–1436 (2004)
Aouf, M.K.: Certain subclasses of multivalent prestarlike functions with negative coefficients. Demonstr. Math. 40(4), 799–814 (2007)
Aouf, M.K., Mostafa, A.O.: On a subclass of n-p-valent prestarlike functions. Comput. Math. Appl. 55, 851–861 (2008)
Aouf, M.K., Mostafa, A.O., Zayed, H.M.: Subordination and superordination properties of p-valent functions defined by a generalized fractional differintegral operator. Quaest. Math. 39(4), 545–560 (2016)
Bulboacă, T.: Differential Subordinations and Superordinations. Recent Results. House of Scientific Book Publ., Cluj-Napoca (2005)
Choi, J.H., Saigo, M., Srivastava, H.M.: Some inclusion properties of a certain family of integral operators. J. Math. Anal. Appl. 276(1), 432–445 (2002)
Goyal, S.P., Prajapat, J.K.: A new class of analytic p-valent functions with negative coefficients and fractional calculus operators. Tamsui Oxf. Univ. J. Math. Sci. 20(2), 175–186 (2004)
Hallenbeck, D.J., Ruscheweyh, St: Subordination by convex functions. Proc. Am. Math. Soc. 52, 191–195 (1975)
Kamali, M., Orhan, H.: On a subclass of certian starlike functions with negative coefficients. Bull. Korean Math. Soc. 41(1), 53–71 (2004)
Liu, M.-S.: On certain sufficient condition for starlike functions. Soochow J. Math. 29, 407–412 (2003)
Miller, S.S., Mocanu, P.T.: Differential subordinations and univalent functions. Mich. Math. J. 28(2), 157–171 (1981)
Miller, S.S., Mocanu, P.T.: Univalent solutions of Briot–Bouquet differential equations. J. Differ. Equ. 58, 297–309 (1985)
Miller, S.S., Mocanu, P.T.: Differential Subordination, Theory and Applications. Series on Monographs and Textbooks in Pure and Applied Mathematics, vol. 225. Marcel Dekker Inc., New York (2000)
Mocanu, P.T., Oros, Gh: A sufficient condtion for starlikeness of order \(\alpha \). Int. J. Math. Math. Sci. 28(9), 557–560 (2001)
Owa, S.: On the distortion theorems. I. Kyungpook Math. J. 18, 53–59 (1978)
Owa, S., Srivastava, H.M.: Univalent and starlike generalized hypergeometric functions. Can. J. Math. 39, 1057–1077 (1987)
Patel, J., Mishra, A.K., Srivastava, H.M.: Classes of multivant analytic functions involving the Dziok–Srivastava operator. Comput. Math. Appl. 54, 599–616 (2007)
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)
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)
Sălăgean, G.S.: Subclasses of univalent functions. In: Complex Analysis—Fifth Romanian Finnish Seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math., vol. 1013, pp. 362–372. Springer, Berlin
Seoudy, T.M., Aouf, M.K.: Subclasses of p-valent functions of bounded boundary rotation involving the generalized fractional differintegral operator. C. R. Acad. Sci. Paris Ser. I 351, 787–792 (2013)
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)
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)
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)
Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, Gourth edn. Cambridge Univ. Press, Cambridge (1927)
Wilken, D.R., Feng, J.: A remark on convex and starlike functions. J. Lond. Math. Soc. (Ser. 2) 21, 287–290 (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mostafa, A.O., Aouf, M.K., Zayed, H.M. et al. Multivalent functions associated with Srivastava–Saigo–Owa fractional differintegral operator. RACSAM 112, 1409–1429 (2018). https://doi.org/10.1007/s13398-017-0436-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13398-017-0436-1
Keywords
- Differential subordination
- p-valent functions
- The Srivastava–Saigo–Owa fractional differintegral operator