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In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using a,b,c∈ℝ, c≠0,−1,−2,…. The study done in this paper extends the results on the univalence of the considered function taking a,b,c∈ℂ, with c≠0,−1,−2,… two criteria being stated in the corollaries of the proved theorems. An interpretation of the univalence results from the sets inclusion view is also given, underlining the geometrical properties of the outcomes. Examples showing how the univalence results can be applied are also included.

Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities