×

zbMATH — the first resource for mathematics

Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava linear operator. (English) Zbl 1204.30008
Summary: Differential subordination and superordination results are obtained for analytic functions in the open unit disk which are associated with the Dziok-Srivastava linear operator. These results are obtained by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aghalary, R.; Ali, R.M.; Joshi, S.B.; Ravichandran, V., Inequalities for analytic functions defined by certain linear operator, Internat. J. math. sci., 4, 2, 267-274, (2005) · Zbl 1266.30016
[2] R.M. Ali, R. Chandrashekar, S.K. Lee, V. Ravichandran, A. Swaminathan, Differential sandwich theorem for multivalent analytic functions associated with the Dziok-Srivastava operator, Tamsui Oxford J. Math. Sci., to appear. · Zbl 1254.30024
[3] R.M. Ali, R. Chandrashekar, S.K. Lee, V. Ravichandran, A. Swaminathan, Differential sandwich theorem for multivalent meromorphic functions associated with the Liu-Srivastava operator, preprint. · Zbl 1236.30023
[4] Ali, R.M.; Ravichandran, V.; Seenivasagan, N., Differential subordination and superordination of analytic functions defined by the multiplier transformation, Math. inequal. appl., 12, 1, 123-139, (2009) · Zbl 1170.30008
[5] R.M. Ali, V. Ravichandran, N. Seenivasagan, Subordination and superordination on Schwarzian derivatives, J. Inequal. Appl. (2008), Art. ID 12328, 18pp. · Zbl 1165.30309
[6] Ali, R.M.; Ravichandran, V.; Seenivasagan, N., On subordination and superordination of the multiplier transformation for meromorphic functions, Bull. malays. math. sci. soc. (2), 33, 2, 311-324, (2010) · Zbl 1189.30009
[7] Ali, R.M.; Ravichandran, V.; Seenivasagan, N., Subordination and superordination of the liu – srivastava linear operator on meromorphic functions, Bull. malays. math. sci. soc. (2), 31, 2, 193-207, (2008) · Zbl 1151.30016
[8] Aouf, M.K.; Hossen, H.M.; Lashin, A.Y., An application of certain integral operators, J. math. anal. appl., 248, 2, 475-481, (2000) · Zbl 0963.30001
[9] Aouf, M.K.; Hossen, H.M.; Lashin, A.Y., An application of certain linear operator, Bull. Korean math. soc., 37, 4, 765-770, (2000) · Zbl 0978.30008
[10] Bernardi, S.D., Convex and starlike univalent functions, Trans. amer. math. soc., 135, 429-446, (1969) · Zbl 0172.09703
[11] Carlson, B.C.; Shaffer, D.B., Starlike and prestarlike hypergeometric functions, SIAM J. math. anal., 15, 4, 737-745, (1984) · Zbl 0567.30009
[12] Dziok, J.; Srivastava, H.M., Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral transforms spec. funct., 14, 7-18, (2003) · Zbl 1040.30003
[13] Hohlov, Yu.E., Operators and operations in the class of univalent functions, Izv. vys. Uebn. zaved. mat., 10, 83-89, (1978)
[14] Kim, Y.C.; Srivastava, H.M., Inequalities involving certain families of integral and convolution operators, Math. inequal. appl., 7, 2, 227-234, (2004) · Zbl 1062.30015
[15] Libera, R.J., Some classes of regular univalent functions, Proc. amer. math. soc., 16, 755-758, (1965) · Zbl 0158.07702
[16] Livingston, A.E., On the radius of univalence of certain analytic functions, Proc. amer. math. soc., 17, 352-357, (1966) · Zbl 0158.07701
[17] Miller, S.S.; Mocanu, P.T., Differential subordinations, (2000), Dekker New York · Zbl 0954.34003
[18] Miller, S.S.; Mocanu, P.T., Subordinants of differential superordinations, Complex var. theory appl., 48, 10, 815-826, (2003) · Zbl 1039.30011
[19] Owa, S., On the distortion theorems. I, Kyungpook math. J., 18, 1, 53-59, (1978) · Zbl 0401.30009
[20] Owa, S.; Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canad. J. math., 39, 5, 1057-1077, (1987) · Zbl 0611.33007
[21] Ruscheweyh, S., New criteria for univalent functions, Proc. amer. math. soc., 49, 109-115, (1975) · Zbl 0303.30006
[22] H.M. Srivastava, Some families of fractional derivative and other linear operators associated with analytic, univalent, and multivalent functions, in: Analysis and its Applications (Chennai, 2000), Allied Publ., New Delhi, 2001, pp. 209-243. · Zbl 1006.30012
[23] Srivastava, H.M.; Yang, D.-G.; Xu, N.-E., Subordinations for multivalent analytic functions associated with the dziok – srivastava operator, Integral transforms spec. funct., 20, 7-8, 581-606, (2009) · Zbl 1170.30006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.