[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2011.48.1.051

CLASS-MAPPING PROPERTIES OF THE HOHLOV OPERATOR

Mishra, Akshaya K. (DEPARTMENT OF MATHEMATICS BERHAMPUR UNIVERSITY)
Panigrahi, Trailokya (DEPARTMENT OF MATHEMATICS TEMPLECITY INSTITUTE OF TECHNOLOGY AND ENGINEERING F/12, IID CENTRE KNOWLEDGE CAMPUS)

Publication Information

Bulletin of the Korean Mathematical Society / v.48, no.1, 2011 , pp. 51-65 More about this Journal

Abstract

In the present paper sufficient conditions, in terms of hyper-geometric inequalities, are found so that the Hohlov operator preserves a certain subclass of close-to-convex functions (denoted by $R^{\tau}$ (A, B)) and transforms the classes consisting of k-uniformly convex functions, k-starlike functions and univalent starlike functions into $\cal{R}^{\tau}$ (A, B).

Keywords

univalent; k-uniformly convex; parabolic starlike; hypergeometric series; Hadamard product; Hohlov operator;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)

Reference

1	H. M. Srivastava, A. K. Mishra, and M. K. Das, A nested class of analytic functions defined by fractional calculus, Commun. Appl. Anal. 2 (1998), no. 3, 321-332.
2	H. M. Srivastava, A. K. Mishra, and M. K. Das, A unified operator in fractional calculus and its applications to a nested class of analytic functions with negative coefficients, Complex Variables Theory Appl. 40 (1999), no. 2, 119-132. DOI ScienceOn
3	H. M. Srivastava, A. K. Mishra, and M. K. Das, A class of parabolic starlike functions defined by means of a certain fractional derivative operator, Fract. Calc. Appl. Anal. 6 (2003), no. 3, 281-298.
4	K. K. Dixit and S. K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math. 26 (1995), no. 9, 889-896.
5	P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 259. Springer-Verlag, New York, 1983.
6	A. Gangadharan, T. N. Shanmugam, and H. M. Srivastava, Generalized hypergeometric functions associated with k-uniformly convex functions, Comput. Math. Appl. 44 (2002), no. 12, 1515-1526. DOI ScienceOn
7	A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601. DOI ScienceOn
8	A. W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56 (1991), no. 1, 87-92.
9	Ju. E. Hohlov, Operators and operations on the class of univalent functions, Izv. Vyssh. Uchebn. Zaved. Mat. 1978 (1978), no. 10, 83-89.
10	S. Kanas and H. M. Srivastava, Linear operators associated with k-uniformly convex functions, Integral Transform. Spec. Funct. 9 (2000), no. 2, 121-132. DOI
11	S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 (1999), no. 1-2, 327-336. DOI ScienceOn
12	S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), no. 4, 647-657.
13	W. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math. 57 (1992), no. 2, 165-175.
14	K. S. Padmanabhan, On a certain class of functions whose derivatives have a positive real part in the unit disc, Ann. Polon. Math. 23 (1970), 73-81.
15	S. Ponnusamy and F. Ronning, Starlikeness properties for convolutions involving hypergeometric series, Ann. Univ. Mariae Curie-Sklodowska Sect. A 52 (1998), no. 1, 141-155.
16	H. M. Srivastava and A. K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Comput. Math. Appl. 39 (2000), no. 3-4, 57-69. DOI
17	L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137-152. DOI
18	T. R. Caplinger and W. M. Causey, A class of univalent functions, Proc. Amer. Math. Soc. 39 (1973), 357-361. DOI ScienceOn
19	F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 189-196. DOI ScienceOn
20	H. M. Srivastava and P. W. Karlson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Series: Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, 1985.
21	H. M. Srivastava and A. K. Mishra, A fractional differintegral operator and its applications to a nested class of multivalent functions with negative coefficients, Adv. Stud. Contemp. Math. (Kyungshang) 7 (2003), no. 2, 203-214.