SOME PROPERTIES OF CERTAIN SUBCLASSES OF MEROMORPHIC P-VALENT INTEGRAL OPERATORS

Year 2014, Volume: 4 Issue: 1, 62 - 66, 01.06.2014

Deborah Olufunmilayo Makinde

Abstract

For meromorphic p-valent function of the form fi z = 1−α z−w p + ∑∞ n=2 a i n z− w n , α < 1, which are analytic in the punctured unit disk z : 0 < |z −w| < 1 with a pole of order p at w, a class Γp β ζ1, ζ2; γ is introduced and some properties for Γp α ζ1, ζ2; γ of fi z in relatioon to the coefficient bounds, convex combination and convolution were discussed.

Keywords

Analytic, Coefficient bound, Convex combination, Meromorphic, p-valent, Integral operator.

References

• O. Altintas, and S. Owa, On soem subclassess of univalent functions with negative coefficient, Pusan Kyongnam Math. J. 4 (1988) 41-46.
• D. Hur and G.H. Oh, On certain class of analytic functions with negative ciefficients, Pusan Kyongnam Math. J. 5(19890), 69-80.
• S. Kanas and F.Ronnig, Unifromly Starlike and conves functions and other related classes of univalent functions, Ann Universitym Narue Curie-Sklodowska Section A,53(1999), 95-105.
• H.S. Kim and S.K. Lee, On soem classes of univalent functions, Math Japan, 32(987), 781-796.
• D.O Makinde and T.O. Opoola, On sufficient condition fo starlikeness, General Mathematics 18(3) 2010, 30-35.
• D.O. Makinde, On a certain family of meromorphic functions with positive coefficients, Acta Univer- sitatis Apulensis (submitted).
• D.O. Makinde and A.T. Oladipo, Some properties of certain subclasses of univalent integral operator. Journal of Sientia Magna (accepted)
• N. Seenivasagan, Sufficient conditions for univalence, Applied Mathemaitics E-notes, 8,2008, 30-35.
• F. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc, 51 (1975),109- 116.
• Xiao-Fei Li and An-Ping Wang, Some properties of some subclassess of univalent functions, Applied Mathematical Sciences, 6(54) (2012) 2687-2693.