Some Inequalities Associated with a Linear Operator Defined for a Class of Multivalent Functions

Volume 4, Issue 4, 2003

Article 70

SOME INEQUALITIES ASSOCIATED WITH A LINEAR OPERATOR DEFINED FOR A CLASS OF MULTIVALENT FUNCTIONS

V. RAVICHANDRAN, N. SEENIVASAGAN AND H.M. SRIVASTAVA

DEPARTMENT OF COMPUTER APPLICATIONS
SRI VENKATESWARA COLLEGE OF ENGINEERING
SRIPERUMBUDUR 602105, TAMIL NADU,
INDIA.
E-Mail: vravi@svce.ac.in

DEPARTMENT OF MATHEMATICS
SINDHI COLLEGE
123 P.H. ROAD, NUMBAL
CHENNAI 600077, TAMIL NADU,
INDIA.
E-Mail: vasagan2000@yahoo.co.in

DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF VICTORIA
VICTORIA, BRITISH COLUMBIA V8W 3P4
CANADA.
E-Mail: harimsri@math.uvic.caURL: http://www.math.uvic.ca/faculty/harimsri/

Received 15 September, 2003; Accepted 17 September, 2003.
Communicated by: Th. M. Rassias

ABSTRACT. The authors derive several inequalities associated with differential subordinations between analytic functions and a linear operator defined for a certain family of p-valent functions, which is introduced here by means of this linear operator. Some special cases and consequences of the main results are also considered.

Key words:
Analytic functions, Univalent and multivalent functions, Differential subordination, Schwarz function, Ruscheweyh derivatives, Hadamard product (or convolution), Linear operator, Convex functions, Starlike functions.

2000 Mathematics Subject Classification:
Primary 30C45.

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