Sandwich theorems involving fractional integrals applied to the q -analogue of the multiplier transformation

Abstract

In this paper, the research discussed involves fractional calculus applied to a $ q $-operator. Fractional integrals applied to the $ q $-analogue of the multiplier transformation gives a new operator, and the research is conducted applying the differential subordination and superordination theories. The best dominant and the best subordinant are obtained by the theorems and corollaries discussed. Combining the results from the both theories, sandwich-type results are presented as a conclusion of this research.

Keywords

• fractional integral of $ q $-analogue of multiplier transformation
• differential subordination
• differential superordination
• best dominant
• best subordinant