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New Symmetric Differential and Integral Operators Defined in the Complex Domain

1,*,† and 2,†
1
Cloud Computing Center, University Malaya, Kuala Lumpur 50603, Malaysia
2
Center for Modelling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(7), 906; https://doi.org/10.3390/sym11070906
Received: 17 May 2019 / Revised: 15 June 2019 / Accepted: 2 July 2019 / Published: 12 July 2019
(This article belongs to the Special Issue Integral Transformations, Operational Calculus and Their Applications)
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PDF [257 KB, uploaded 12 July 2019]

Abstract

The symmetric differential operator is a generalization operating of the well-known ordinary derivative. These operators have advantages in boundary value problems, statistical studies and spectral theory. In this effort, we introduce a new symmetric differential operator (SDO) and its integral in the open unit disk. This operator is a generalization of the Sàlàgean differential operator. Our study is based on geometric function theory and its applications in the open unit disk. We formulate new classes of analytic functions using SDO depending on the symmetry properties. Moreover, we define a linear combination operator containing SDO and the Ruscheweyh derivative. We illustrate some inclusion properties and other inequalities involving SDO and its integral. View Full-Text
Keywords: univalent function; symmetric differential operator; unit disk; analytic function; subordination univalent function; symmetric differential operator; unit disk; analytic function; subordination
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ibrahim, R.W.; Darus, M. New Symmetric Differential and Integral Operators Defined in the Complex Domain. Symmetry 2019, 11, 906.

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