Third-order strong differential subordinations involving fractional integral of confluent (Kummer) and Gaussian hypergeometric functions

Preluca, Lavinia Florina

doi:10.2478/gm-2024-0003

Abstract

For the study presented in this paper, the concepts specific to strong differential subordination theory, introduced for the second-order differential subordination case, are extended for the third-order differential subordination case. The general results presented in the first theorem proved in this investigation are applied considering the prolific operators recently introduced as the fractional integral of confluent (Kummer) hypergeometric function and as the fractional integral of Gaussian hypergeometric function, respectively, adapted considering the extra parameter imposed by the strong differential subordination theory and new third-order differential subordinations are investigated. Simple examples are also constructed but it is hoped that the results given here would inspire future similar studies for applying the new third-order strong differential subordination results using other known operators adapted in order to fit this new context.

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Third-order strong differential subordinations involving fractional integral of confluent (Kummer) and Gaussian hypergeometric functions

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