New Classes of Non-normalized Meromorphically Multivalent Functions
DOI:
https://doi.org/10.5644/SJM.03.2.02Keywords:
Differential operators, non-normalized function, analytic function, meromorphically multivalent function, punctured unit disk, meromorphically multivalent starlike functions, meromorphically multivalent convex functions, Jack's LemmaAbstract
Making use of certain differential operators, this paper
introduces two new classes: $${\mathcal
M}_{m,n,\delta}^{\kappa}(q;p)\;\; \; \mbox{and} \;\;\;{\mathcal
SK}_{m,n, \delta}^{\kappa}(q;p)$$ which consist of non-normalized meromorphically multivalent funcons with complex coefficients in the punctured unit disk. A theorem is established concerning an inclusion property for the above classes, and in the concluding section, several consequences of the main result are pointed out.
2000 Mathematics Subject Classification. Primary 30C45; Secondary 32A20, 30A10
Downloads
References
M.-P. Chen, H. Irmak, H. M. Srivastava and C.-S. Yu, Certain subclasses of meromorphically univalent functions with negative or positive coefficients, Pan Amer. Math. J., 6 (2) (1996), 65–77.
M.-P. Chen, H. Irmak, and H. M. Srivastava and C.-S. Yu, Some subclasses of meromorphically multivalent functions with negative or positive coefficients, Pan Amer. Math. J., 7 (4) (1997), 53–72.
M.-P. Chen, H. Irmak and H. M. Srivastava, Some families of multivalently analytic functions with negative coefficients, J. Math. Anal. Appl., 214 (1997), 674–690.
P. L. Duren, Univalent Functions, Grundlehren der Mathematishen Wissenschaften, Bd. 259, Springer-Verlag, Berlin, Heidelberg and Tokyo, 1983.
J. Dziok and H. Irmak, Certain operators and inequalities and their applications to meromorphically multivalent functions, Demonstratio Math., 36 (2003), 839–846.
J. Dziok and H. Irmak, Some families of meromorphically multivalent functions and their applications, Zeszyty Nauk. Politech. Rzeszowskiej Mat., 27 (2004), 19–23.
A. W. Goodman, Univalent Functions, Vols. I and II, Polygonal Publishing House, Washington, New Jersey, 1983.
H. Irmak, S. H. Lee and N. E. Cho, Some families of multivalently analytic functions with negative coefficients, Kyungpook Math. J., 37 (1) (1997), 43–51.
H. Irmak and R. K. Raina, On certain classes of functions associated with multivalently analytic and multivalently meromorphic functions, Soochow J. Math., 32 (3) (2006), 413–419.
H. Irmak, N. E. Cho, O. F. C¸ etin and R. K. Raina, ¨ Certain inequalities involving
meromorphically multivalent functions, Hacet. Bull. Nat. Sci. Eng. Ser. B, 30 (2001),
–43.
H. Irmak, A class of p-valently analytic functions with positive coefficients, Tamkang
J. Math., 27(4) (1996), 315–322.
I. S. Jack, Functions starlike and convex of order α, J. London Math. Soc., 3 (1971),
–474.
J.-L. Liu and H. M. Srivastava, A lineer operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl., 259 (2001), 566–581.
H. M. Srivastava and S. Owa, Editors, Current Topics in Analytic Function Theory,
World Scientific Publication, Singapore, 1992.
