Noor, Khalida Inayat On generalized \(q\)-Bazilevic functions. (English) Zbl 1378.30004 J. Adv. Math. Stud. 10, No. 3, 418-424 (2017). Summary: Let \(S^*\) and \(C\), respectively, be the classes of starlike and convex univalent functions. The \(q\)-derivative of a function, analytic in the open unit disk is defined by \(D_q f(z)=\frac{f(qz)-f(z)}{(q-1)z}\), \(z \neq 0\), and \(D_q f(0)=f'(0)\), \(q \in (0, 1)\). As \(q \to 1^-\), \(D_q f(z) \to f'(z)\). This concept has been used to define certain classes of analytic functions such as \(S^*_q\) of \(q\)-starlike and \(C_q\) of \(q\)-convex functions with the property \(\bigcap\limits_{0<q<1}= S^*_q=S^*\) and \(\bigcap\limits_{0<q<1} C_q=C\). In this paper, we introduce a new class of \(q\)-Bazilevic functions of type \(\beta\) which contains \(S^*_q\) and \(C_q\) as special cases. Inclusion results and mappings properties of certain \(q\)-integral operators are studied. Cited in 2 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 30C10 Polynomials and rational functions of one complex variable Keywords:convex; star-like; \(q\)-star-like; Bazilevic functions; subordination PDFBibTeX XMLCite \textit{K. I. Noor}, J. Adv. Math. Stud. 10, No. 3, 418--424 (2017; Zbl 1378.30004)