Browse > Article
http://dx.doi.org/10.14317/jami.2021.133

HIGHER ORDER CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH RUSCHEWEYH DERIVATIVE OPERATOR  

NOOR, KHALIDA INAYAT (Department of Mathematics, COMSATS University Islamabad)
SHAH, SHUJAAT ALI (Department of Mathematics, COMSATS University Islamabad)
Publication Information
Journal of applied mathematics & informatics / v.39, no.1_2, 2021 , pp. 133-143 More about this Journal
Abstract
The purpose of this paper is to introduce and study certain subclasses of analytic functions by using Ruscheweyh derivative operator. We discuss various of interesting properties such as, necessary condition, arc length problem and growth rate of coefficient of newly defined class. Also rate of growth of Hankel determinant will be estimated.
Keywords
Close-to-convex functions; Ruschweyh derivative operator; Janowski's functions; Conic domains;
Citations & Related Records
연도 인용수 순위
  • Reference
1 C. Pommerenke, On the coefficients and Hankel determinant of univalent functions, J. London Math. Soc. 41 (1966), 111-122.   DOI
2 C. Pommerenke, On starlike and close-to-convex functions, Proc. London Math. Soc. 13 (1963), 290-304.   DOI
3 D.A. Brannan, On functions of bounded boundary rotation, Proc. Edinburg Math. Soc. 16 (1968), 339-347.   DOI
4 G.M. Golusin, On distortion theorem and coefficients of univalent functions, Math. Sb. 19 (1946), 183-203.
5 A.W. Goodman, On close-to-convex functions of higher order, Ann. Univ. Sci. Budapest, Eotous Sect. Math. 25 (1972), 17-30.
6 W.K. Hayman, On the second Hankel determinant of mean univalent functions, Proc. London Math. Soc. 18 (1968), 77-84.   DOI
7 W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28 (1973), 297-326.   DOI
8 S. Kanas and A. Wisniowska, Conic domain and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), 647-657.
9 S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Math. 105 (1999), 327-336.   DOI
10 K.I. Noor, Hankel determinant problem for functions of bounded boundary rotations, Rev. Roum. Math. Pures Appl. 28 (1983), 731-739.
11 K.I. Noor, On a generalization of close-to-convexity, Int. J. Math. Math. Sci. 6 (1983), 327-334.   DOI
12 K.I. Noor, Some properties of analytic functions with bounded radius rotation, Complex Var. Elliptic Equ. 54 (2009), 865-877.   DOI
13 K.I. Noor, and M.A. Noor, On generalized close-to-convex functions, Appl. Math. Inf. Sci. 9 (2015), 3147-3152.
14 K.I. Noor, On the Hankel determinant of close-to-convex univalent functions, Inter. J. Math. Sci. 3 (1980), 447-481.
15 K.I. Noor, On the Hankel determinant problem for strongly close-to-convex functions, J. Natu. Geom. 11 (1997), 29-34.
16 K.I. Noor and M.A. Noor, Higher order close-to-convex functions related with conic domains, Appl. Math. Inf. Sci. 8 (2014), 2455-2463.   DOI
17 J.W. Noonan and D.K. Thomas, On the Hankel determinant of areally mean p-valent functions, Proc. London Math. Soc. 25 (1972), 503-524.
18 K.S. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31 (1975), 311-323.   DOI
19 S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.   DOI