IJPAM: Volume 109, No. 3 (2016)

PROPERTIES OF THE MODIFIED CAPUTO'S DERIVATIVE
OPERATOR FOR CERTAIN ANALYTIC FUNCTIONS

Jamal Y. Salah
Department of Basic Sciences
College of Applied Sciences
A'Sharqiyah University
Ibra, OMAN

Abstract. In this paper, a class $ A_{\eta,\lambda}(\alpha ,\beta ,\gamma ) $ of analytic functions involving the integral operator $ J_{\eta ,\lambda } f\left(z\right)=z+\sum _{n=2}^{\infty }\frac{\left(\Gamma \... ...amma \left(n+\eta -\lambda +1\right)\Gamma \left(n-\eta +1\right)} a_{n} z^{n} $,given by Salah and Darus in [5] is defined. The extreme points for this class are provided, the coefficient bounds and radii of univalency and starlikeness are also provided.

Received: June 24, 2016

Revised: August 31, 2016

Published: October 1, 2016

AMS Subject Classification: 30C45, 30C50

Key Words and Phrases: Caputo's differentiation operator, univalency, starlikeness, Hadamard product
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J. Salah, M. Darus, A subclass of uniformly convex functions associated with fractional calculus operator involving Caputo's fractional differentiation, Acta. Univ. Apl., 24 (2010), 295-306.

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DOI: 10.12732/ijpam.v109i3.14 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: 2016
Volume: 109
Issue: 3
Pages: 665 - 671


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