**1. Introduction**

The introduction of the fuzzy set concept by Lotfi A. Zadeh, in the paper "Fuzzy Sets" [1] in 1965, did not sugges<sup>t</sup> the extraordinary evolution of the concept which followed. Received with distrust at first, the concept is very popular nowadays, being adapted to many research topics. Mathematicians were also interested in embedding the concept of fuzzy set in their research and it was indeed included in many mathematical approaches. The review paper included in the present special issue, devoted to the celebration of the 100th anniversary of Zadeh's birth [2], shows how fuzzy set theory has evolved related to certain branches of science, and points out the contribution of one of Zadeh's disciples, Professor I. Dzitac, to the development of soft computing methods connected with fuzzy set theory. Professor I. Dzitac has celebrated his friendship with the multidisciplinary scientist, Lotfi A. Zadeh, by writing the introductory paper of a special issue on fuzzy logic dedicated to the centenary of Zadeh's birth [3].

As far as complex analysis is concerned, fuzzy set theory has been included in studies related to geometric function theory in 2011, when the first paper appeared introducing the notion of subordination in fuzzy set theory [4] which has had its inspiration in the classical aspects of subordination introduced by Miller and Mocanu [5,6]. The next papers published followed the line of research set by Miller and Mocanu and referred to fuzzy differential subordination, adapting notions from the already well-established theory of differential subordination [7–9]. The idea was soon picked up by researchers in geometric function theory and all the classical lines of research in this topic were adapted to the new fuzzy aspects. A review paper published in 2017 [10] included in its references the first published papers related to this topic, validating its development. The dual notion of fuzzy differential superordination was also introduced in 2017 [11].

An important topic in geometric function theory is conducting studies which involve operators. Such studies for obtaining new fuzzy subordination results were published soon after the notion was introduced, in 2013 [12], continued during the next years [13–16] and later added the superordination results [17–19]. During the last years, many papers were

**Citation:** Oros, G.I. Fuzzy Differential Subordinations Obtained Using a Hypergeometric Integral Operator. *Mathematics* **2021**, *9*, 2539. https://doi.org/10.3390/math9202539

Academic Editors: Ioan Dzitac and Sorin Nadaban

Received: 14 September 2021 Accepted: 6 October 2021 Published: 10 October 2021

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published which show that the research on this topic is in continuous development process and we mention only a few here [20–24].

Following this line of research, a new hypergeometric integral operator is introduced in this paper using a confluent (or Kummer) hypergeometric function and having, as inspiration, the operator studied by Miller, Mocanu and Reade in 1978, by taking specific values for parameters involved in its definition. Fuzzy differential subordinations are obtained and the fuzzy best dominants are given, which facilitate obtaining sufficient conditions for univalence of this operator.
