IJPAM: Volume 87, No. 1 (2013)

A FAMILY OF p-VALENT ANALYTIC FUNCTIONS
DEFINED BY A FRACTIONAL CALCULUS OPERATOR

Mamta Pathak1, Poonam Sharma2
1Babu Banarasi Das Group of Educational Institutions
Faizabad Road, Lucknow, INDIA
2Deparment of Mathematics and Astronomy
University of Lucknow
Lucknow, INDIA


Abstract. In this Paper a family $S(\alpha ,\beta ,\mu ,p)$ of p-valent analytic functions involving fractional calculus operator $\Omega _{z}^{\mu ,p}$ is studied and a sufficient coefficient condition for functions belonging to the family $S(\alpha ,\beta ,\mu ,p)$ is proved and it is shown that this coefficient condition is necessary for its subfamily $TS(\alpha ,\beta ,\mu
,p)$. Coefficient estimate, growth theorem and results on partial sums are obtained for the family $S(\alpha ,\beta ,\mu ,p)$. Also an integral inequality is proved for functions belonging to the family $TS(\alpha ,\beta
,\mu ,p).$

Received: May 12, 2013

AMS Subject Classification: 30C45, 30C55

Key Words and Phrases: analytic functions, starlike function, convex functions, partial sums, integral mean inequality

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DOI: 10.12732/ijpam.v87i1.7 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 1