# Article ID: MTJPAM-D-20-00037

## Title: About a Subclass of Analytic Functions Defined by a Fractional Integral Operator

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00037; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 200-210

Document Type: Research Paper

Author(s): Alb Lupaş Alina a

Received: 28 October 2020, Accepted: 28 February 2021, Published: 25 April 2021.

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Abstract

In this paper we have introduced and studied the subclass $\mathcal{D}_{m,n}(\delta ,\lambda ,d,\gamma ,\beta )$ using the fractional integral operator associated with a linear differential operator. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class  $\mathcal{D}_{m,n}(\delta ,\lambda ,d,\gamma ,\beta )$.

Keywords: Analytic functions, Univalent functions, Radii of starlikeness and convexity, Neighborhood property

References:
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2. A. Alb Lupaş, Properties on a subclass of univalent functions defined by using Sălăgean operator and Ruscheweyh derivative, J. of Comput. Anal. Appl. 21 (7), 1213-1217, 2016.
3. A. Alb Lupaş, Inequalities for Analytic Functions Defined by a Fractional Integral Operator, Frontiers in functional equations and analytic inequalities, Springer, 731-745, 2020.
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5. S. M. El-Deeb, A. Alb Lupaş, Fuzzy Differential Subordinations Connected with Convolution, submitted 2020.