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Classes of meromorphically multivalent functions associated with the generalized hypergeometric function. (English) Zbl 1049.30008
Making use of a linear operator, which is defined here by means of a Hadamard product (or convolution) involving the generalized hypergeometric function, the authors introduce and investigate two novel classes of meromorphically multivalent functions. In recent years, many important properties and charatcteristics of various interesting subclasses of the class $\Sigma_{p}$ of meromorphically $p$-valent functions were investigated extensively by (among others) Aouf et al. Joshi and Srivastava, Kulkarni et al., Liu and Srivastava, Owa et al., Srivastava et al., Uralegaddi and Somanatha, and Yang. The main object of this paper is to present several inclusion and other properties of functions in the classes $\Omega_{p, q, s}(\alpha_{1}; A, B)$ and $\Omega_{p, q,s}^{+}(\alpha_{1}; A, B)$ which the authors introduced here. They also apply the familiar concept of neighborhoods of analytic functions to meromorphically $p$-valent functions in the class $\Sigma_{p}$. In the first results the authors apply the well-known Jack’s Lemma.

MSC:
30C45Special classes of univalent and multivalent functions
33C20Generalized hypergeometric series, ${}_pF_q$
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References:
[1] Dziok, J.; Srivastava, H. M.: Classes of analytic functions associated with the generalized hypergeometric function. Appl. math. Comput. 103, 1-13 (1999) · Zbl 0937.30010
[2] Dziok, J.; Srivastava, H. M.: Certain subclasses of analytic functions associated with the generalized hypergeometric function. Integral transform. Spec. funct. 14, 7-18 (2003) · Zbl 1040.30003
[3] Gangadharan, A.; Shanmugam, T. N.; Srivastava, H. M.: Generalized hypergeometric functions associated with k-uniformly convex functions. Computers math. Applic. 44, No. 12, 1515-1526 (2002) · Zbl 1036.33003
[4] Liu, J. -L: Strongly starlike functions associated with the dziok-Srivastava operator. Tamkang J. Math. 35 (2004) · Zbl 1064.30006
[5] Aouf, M. K.; Hossen, H. M.: New criteria for meromorphic p-valent starlike functions. Tsukuba J. Math. 17, 481-486 (1993) · Zbl 0804.30012
[6] Aouf, M. K.; Srivastava, H. M.: A new criterion for meromorphically p-valent convex functions of order alpha. Math. sci. Res. hot-line 1, No. 8, 7-12 (1997) · Zbl 0893.30011
[7] Joshi, S. B.; Srivastava, H. M.: A certain family of meromorphically multivalent functions. Computers math. Applic. 38, No. 3/4, 201-211 (1999) · Zbl 0959.30010
[8] Kulkarni, S. R.; Naik, U. H.; Srivastava, H. M.: A certain class of meromorphically p-valent quasi-convex functions. Pan. amer. Math. J. 8, No. 1, 57-64 (1998) · Zbl 0957.30013
[9] Liu, J. -L; Srivastava, H. M.: A linear operator and associated families of meromorphically multivalent functions. J. math. Anal. appl. 259, 566-581 (2001) · Zbl 0997.30009
[10] Liu, J. -L; Srivastava, H. M.: Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions. Appl. math. Lett. 16, No. 1, 13-16 (2003) · Zbl 1057.30013
[11] Mogra, M. L.: Meromorphic multivalent functions with positive coefficients. I. Math. japon. 35, 1-11 (1990) · Zbl 0705.30019
[12] Mogra, M. L.: Meromorphic multivalent functions with positive coefficients. II. Math. japon. 35, 1089-1098 (1990) · Zbl 0718.30009
[13] Owa, S.; Darwish, H. E.; Aouf, M. K.: Meromorphic multivalent functions with positive and fixed second coefficients. Math. japon. 46, 231-236 (1997) · Zbl 0895.30009
[14] Srivastava, H. M.; Hossen, H. M.; Aouf, M. K.: A unified presentation of some classes of meromorphically multivalent functions. Computers math. Applic. 38, No. 11/12, 63-70 (1999) · Zbl 0978.30011
[15] Uralegaddi, B. A.; Somanatha, C.: New criteria for meromorphic starlike univalent functions. Bull. austral. Math. soc. 43, 137-140 (1991) · Zbl 0708.30016
[16] Uralegaddi, B. A.; Somanatha, C.: Certain classes of meromorphic multivalent functions. Tamkang J. Math. 23, 223-231 (1992) · Zbl 0769.30012
[17] Yang, D. -G: Subclasses of meromorphically p-valent convex functions. J. math. Res. exposition 20, 215-219 (2000) · Zbl 0964.30009
[18] Yang, D. -G: On new subclasses of meromorphic p-valent functions. J. math. Res. exposition 15, 7-13 (1995) · Zbl 1108.30309
[19] Duren, P. L.: Univalent functions, grundlehren der mathematischen wissenschaften. 259 (1983)
[20] Srivastava, H. M.; Owa, S.: Current topics in analytic function theory. (1992) · Zbl 0976.00007
[21] Goodman, A. W.: Univalent functions and nonanalytic curves. Proc. amer. Math. soc. 8, 598-601 (1957) · Zbl 0166.33002
[22] Ruscheweyh, S.: Neighborhoods of univalent functions. Proc. amer. Math. soc. 81, 521-527 (1981) · Zbl 0458.30008
[23] Jack, I. S.: Functions starlike and convex of order ${\alpha}$. J. London math. Soc., series 2 3, 469-474 (1971) · Zbl 0224.30026
[24] Altintas, O.; Owa, S.: Neighborhoods of certain analytic functions with negative coefficients. Internat. J. Math. and math. Sci. 19, 797-800 (1996) · Zbl 0915.30008
[25] Altintaş, O.; Özkan, Ö; Srivastava, H. M.: Neighborhoods of a class of analytic functions with negative coefficients. Appl. math. Lett. 13, No. 3, 63-67 (2000) · Zbl 0955.30015
[26] Silverman, H.: Univalent functions with negative coefficients. Proc. amer. Math. soc. 51, 109-116 (1975) · Zbl 0311.30007
[27] Srivastava, H. M.; Owa, S.: Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions. Nagoya math. J. 106, 1-28 (1987) · Zbl 0607.30014