Singh, Sukhjit A subordination theorem for spirallike functions. (English) Zbl 0963.30015 Int. J. Math. Math. Sci. 24, No. 7, 433-435 (2000). Let \(G(\lambda)\) denote the class of functions \(f(z)= z+\sum^\infty_{n=2} a_nz^n\), analytic in the unit disk \(E\) and satisfying \[ \sum^\infty_{n=2} [1+(n- 1)\text{sec }\lambda]|a_n|\leq 1,\;\Biggl(|\lambda|< {\pi\over 2}\Biggr). \] Theorem: Let \(f\in G(\lambda)\), \(g\) is analytic in \(E\), \(g(0)= g'(0)- 1= 0\) and \(g(E)\) is convex, \(f*g\) means Hadamard product.Then \({1+ \text{sec }\lambda\over 2(2+\text{sec }\lambda)}(f* g)(z)\) is subordinate to \(g(z)\) in \(E\). The factor \({1+ \text{sec }\lambda\over 2(2+ \text{sec }\lambda)}\) is best possible. Reviewer: J.Waniurski (Lublin) Cited in 13 Documents MSC: 30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination 30C50 Coefficient problems for univalent and multivalent functions of one complex variable 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:satisfying; subordinate PDFBibTeX XMLCite \textit{S. Singh}, Int. J. Math. Math. Sci. 24, No. 7, 433--435 (2000; Zbl 0963.30015) Full Text: DOI EuDML