ON A CERTAIN CLASS OF (_p-)VALENT UNIFORMLY CONVEX FUNCTIONS USING DIFFERENTIAL OPERATOR
1
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this paper, using differential operator, we have introduce new class of p-valent uniformly convex functions in the unit disc U={z:|z|<1} and obtain the coefficient bounds, extreme bounds and radius of starlikeness for the functions belonging to this generalized class. Furthermore,partial sums f_k(z) of functions f(z) in the class S^*(λ, α, β) are considered. The various results obtained in this paper are sharp.
Abstract
In this paper, using differential operator, we have introduce new class of p-valent uniformly convex functions in the unit disc U={z:|z|<1} and obtain the coefficient bounds, extreme bounds and radius of starlikeness for the functions belonging to this generalized class. Furthermore,partial sums f_k(z) of functions f(z) in the class S^*(λ, α, β) are considered. The various results obtained in this paper are sharp.
참고문헌 (13)
- G. Murugusundaramoorthy, "Carlson-Shaffer Operator and their Applications to Certain Subclass of Uniformly Convex Functions", General Mathematics, Gen. Math, 15(4), pp.131~143 (2007)
- G. Ghanim, "A New Subclass of Uniformly Starlike and Covex Functions with Negative Coefficients", Int. Math. Forum, 4(23), pp.1105~1117 (2009)
- A. W. Goodman, "On Uniformly Starlike Function", J. Math Anal. Appl, 155, pp.364~370 (1991)
- A. W. Goodman, "On Uniformly Convex Function", Ann. Polon. Math, 56, pp.87~92 (1991)
- F. Ronning, "Integral Representation for Bounded Starlike Functions", Ann. Polon. Math, 60, pp.289~297 (1995)
- F. Ronning, "Unifromly Convex Functions and a corresponding Class of Starlike Functions", Proc. Amer. Math. Soc, 118, pp.189~196 (1993)
- E. Aqlan, "Classes of K-uniformly Convex and starlike Functions", Tamkang J. Math, 35(3), pp.261~266 (2004)
- H. Silverman, "Partial -Sums of Starlike and Convex Functions", J. Math Anal. Appl, 209, pp.221~227 (1997)
- E. M. Silvia, "Partial Sums of Convex Functions of order", Honston J. Math. Soc, 11(3), pp.397~404 (1985)
- K. G. Subramanian, "Subclasses of Uniformly Convex and Uniformly starlike functions", Math. Japon, 42(3), pp.517~522 (1995)
- K. G. Subramanian, "Classes of Uniformly Starlike Functions", Publ. Math. Debrecen, 53(34), pp.180~186 (1998)
- H. Silverman, "Univalent Functions with negative coefficients", Proc. Amer. Math. Soc, 51, pp.109~116 (1975)
- B. C. Carlson, "Starlike and Prestarlike Hypergeometric Functions", SIAM J. Math. Anal, 78, pp.737~745 (1986)