Fuzzy Differential Subordination and Superordination Results Involving the <i>q</i>-Hypergeometric Function and Fractional Calculus Aspects

Abstract

The concepts of fuzzy differential subordination and superordination were introduced in the geometric function theory as generalizations of the classical notions of differential subordination and superordination. Fractional calculus is combined in the present paper with quantum calculus aspects for obtaining new fuzzy differential subordinations and superordinations. For the investigated fuzzy differential subordinations and superordinations, fuzzy best subordinates and fuzzy best dominants were obtained, respectively. Furthermore, interesting corollaries emerge when using particular functions, frequently involved in research studies due to their geometric properties, as fuzzy best subordinates and fuzzy best dominants. The study is finalized by stating the sandwich-type results connecting the previously proven results.

Keywords

• Riemann–Liouville fractional integral
• <i>q</i>-hypergeometric function
• fuzzy differential subordination
• fuzzy differential superordination
• fuzzy best dominant
• fuzzy best subordinate