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Abstract The study presented in this article involves q -calculus connected to fractional calculus applied in the univalent functions theory. Riemann-Liouville fractional integral of q -hypergeometric function is defined here, and investigations are conducted using the theories of differential subordination and superordination. Theorems and corollaries containing new subordination and superordination results are proved for which best dominants and best subordinants are given, respectively. As an application of the results obtained by the means of the two theories, the statement of a sandwich-type theorem concludes the study.
Lupaş et al. (Sun,) studied this question.