New Developments on the Theory of Third-Order Differential Superordination Involving Gaussian Hypergeometric Function

Georgia Irina Oros and Lavinia Florina Preluca ()
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Georgia Irina Oros: Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania
Lavinia Florina Preluca: Doctoral School of Engineering Sciences, University of Oradea, 410087 Oradea, Romania

Mathematics, 2023, vol. 11, issue 21, 1-15

Abstract: The present research aims to present new results regarding the fundamental problem of providing sufficient conditions for finding the best subordinant of a third-order differential superordination. A theorem revealing such conditions is first proved in a general context. As another aspect of novelty, the best subordinant is determined using the results of the first theorem for a third-order differential superordination involving the Gaussian hypergeometric function. Next, by applying the results obtained in the first proved theorem, the focus is shifted to proving the conditions for knowing the best subordinant of a particular third-order differential superordination. Such conditions are determined involving the properties of the subordination chains. This study is completed by providing means for determining the best subordinant for a particular third-order differential superordination involving convex functions. In a corollary, the conditions obtained are adapted to the special case when the convex functions involved have a more simple form.

Keywords: third-order differential superordination; best subordinant; Gaussian hypergeometric function; subordination chain; convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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