Certain properties of \(q\)-hypergeometric functions (Q1751373)

Summary: The quotients of certain \(q\)-hypergeometric functions are presented as \(g\)-fractions which converge uniformly in the unit disc. These results lead to the existence of certain \(q\)-hypergeometric functions in the class of either \(q\)-convex functions, \(\mathcal{P} \mathcal{C}_q\), or \(q\)-starlike functions \(\mathcal{P} \mathcal{S}_q^{*}\).