Strong Differential Subordinations and Superordinations for Riemann–Liouville Fractional Integral of Extended q -Hypergeometric Function

Alina Alb Lupaş and Georgia Irina Oros ()
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Alina Alb Lupaş: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, Romania

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

Abstract: The notions of strong differential subordination and its dual, strong differential superordination, have been introduced as extensions of the classical differential subordination and superordination concepts, respectively. The dual theories have developed nicely, and important results have been obtained involving different types of operators and certain hypergeometric functions. In this paper, quantum calculus and fractional calculus aspects are added to the study. The well-known q -hypergeometric function is given a form extended to fit the study concerning previously introduced classes of functions specific to strong differential subordination and superordination theories. Riemann–Liouville fractional integral of extended q -hypergeometric function is defined here, and it is involved in the investigation of strong differential subordinations and superordinations. The best dominants and the best subordinants are provided in the theorems that are proved for the strong differential subordinations and superordinations, respectively. For particular functions considered due to their remarkable geometric properties as best dominant or best subordinant, interesting corollaries are stated. The study is concluded by connecting the results obtained using the dual theories through sandwich-type theorems and corollaries.

Keywords: Riemann–Liouville fractional integral; extended q-confluent hypergeometric function; strong differential subordination; strong differential superordination; best dominant; best subordinant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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