Integral Means Inequalities for Fractional Derivatives of Some General Subclasses of Analytic Functions

Volume 3, Issue 5, 2002

Article 66

INTEGRAL MEANS INEQUALITIES FOR FRACTIONAL DERIVATIVES OF SOME GENERAL SUBCLASSES OF ANALYTIC FUNCTIONS

TADAYUKI SEKINE, KAZUYUKI TSURUMI, SHIGEYOSHI OWA AND H.M. SRIVASTAVA

COLLEGE OF PHARMACY
NIHON UNIVERSITY
7-1 NARASHINODAI 7-CHOME, FUNABASHI-SHI
CHIBA 274-8555, JAPAN
E-Mail: tsekine@pha.nihon-u.ac.jp

DEPARTMENT OF MATHEMATICS
TOKYO DENKI UNIVERSITY
2-2 NISIKI-CHO, KANDA, CHIYODA-KU
TOKYO 101-8457, JAPAN
E-Mail: tsurumi@cck.dendai.ac.jp

DEPARTMENT OF MATHEMATICS
KINKI UNIVERSITY
HIGASHI-OSAKA
OSAKA 577-8502, JAPAN.
E-Mail: owa@math.kindai.ac.jp

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

Received 26 June, 2002; Accepted 4 July, 2002.
Communicated by: D.D. Bainov

ABSTRACT.

Integral means inequalities are obtained for the fractional derivatives of order $p+\lambda$ $(0\leqq p\leqq n;$ $0\leqq\lambda <1)$ of functions belonging to certain general subclasses of analytic functions. Relevant connections with various known integral means inequalities are also pointed out.

Key words:
Integral means inequalities, Fractional derivatives, Analytic functions, Univalent functions, Extreme points, Subordination.

2000 Mathematics Subject Classification:
Primary 30C45; Secondary 26A33, 30C80.

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