[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2015.55.2.383

Certain Subclasses of k-Uniformly Starlike and Convex Functions of Order α and Type β with Varying Argument Coefficients

AOUF, MOHAMED KAMAL (Department of Mathematics, Faculty of Science, Mansoura University)
MAGESH, NANJUNDAN (P.G. and Research Department of Mathematics, Govt Arts College for Men)
YAMINI, JAGADESAN (Department of Mathematics, Govt First Grade College)

Publication Information

Kyungpook Mathematical Journal / v.55, no.2, 2015 , pp. 383-394 More about this Journal

Abstract

In this paper, we define two new subclass of k-uniformly starlike and convex functions of order ${\alpha}$ type ${\beta}$ with varying argument of coefficients. Further, we obtain coefficient estimates, extreme points, growth and distortion bounds, radii of starlikeness, convexity and results on modified Hadamard products.

Keywords

Univalent functions; convex functions; starlike functions; uniformly convex functions; uniformly starlike functions;

Citations & Related Records

Reference

1	O. Altintas and S. Owa, On subclasses of univalent functions with negative coefficients, Pusan Kyongnam Math. J., 4(1988), 41-56.
2	R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 28(1)(1997), 17-32.
3	J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14(1)(2003), 7-18. DOI ScienceOn
4	J. Dziok and H. M. Srivastava, A unified class of analytic functions with varying argument of coefficients, Eur. J. Pure Appl. Math., 2(3)(2009), 302-324.
5	R. M. El-Ashwah, M. K. Aouf, A. A. M. Hassan and A. H. Hassan, Certain new classes of analytic functions with varying arguments, J. Complex Anal., 2013, Art. ID 958210, 5 pp.
6	A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1)(1991), 87-92.
7	A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl., 155(2)(1991), 364-370. DOI
8	S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform. Spec. Funct., 9(2)(2000), 121-132. DOI
9	S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math., 105(1-2)(1999), 327-336. DOI ScienceOn
10	S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45(4)(2000), 647-657.
11	N. Magesh, Certain subclasses of uniformly convex functions of order ${\alpha}$ and type ${\beta}$ with varying arguments, J. Egyptian Math. Soc., 21(3)(2013), 184-189. DOI ScienceOn
12	W. C. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(2)(1992), 165-175.
13	G. Murugusundaramoorthy and N. Magesh, On certain subclasses of analytic functions associated with hypergeometric functions, Appl. Math. Lett., 24(4)(2011), 494-500. DOI ScienceOn
14	F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1)(1993), 189-196. DOI ScienceOn
15	S. Shams, S. R. Kulkarni and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci., 53-56(2004), 2959-2961.
16	K. G. Subramanian, T. V. Sudharsan, P. Balasubrahmanyam and H. Silverman, Classes of uniformly starlike functions, Publ. Math. Debrecen, 53(3-4)(1998), 309-315.
17	H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116. DOI ScienceOn
18	H. Silverman, Univalent functions with varying arguments, Houston J. Math., 7(2)(1981), 283-287.
19	Y. J. Sim, O. S. Kwon, N. E. Cho and H. M. Srivastava, Some classes of analytic functions associated with conic regions, Taiwanese J. Math., 16(1)(2012), 387-408.