Swamy, S. R. Some inequalities associated with a linear operator defined for a class of analytic functions. (English) Zbl 1131.30325 JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 6, 6 p. (2006). Summary: We give a sufficient condition on a linear operator \(L_p(a,c)g(z)\) which can guarantee that, for \(\alpha\) a complex number with \(\mathrm{Re}\,\alpha>0\), \[ \mathrm{Re}\left\{(1-\alpha)\frac{L_p(a,c)f(z)}{L_p(a,c)g(z)}+\alpha \frac{L_p(a+1,c)f(z)}{L_p(a+1,c)g(z)}\right\}>\rho,\quad \rho<1, \] in the unit disk \(E\), implies \[ \mathrm{Re}\left\{\frac{L_p(a,c)f(z)}{L_p(a,c)g(z)}\right\}>\rho'>\rho,\quad z\in E. \] Some interesting applications of this result are also given. MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:analytic functions; differential subordination; Ruscheweyh derivatives; linear operator PDFBibTeX XMLCite \textit{S. R. Swamy}, JIPAM, J. Inequal. Pure Appl. Math. 7, No. 1, Paper No. 6, 6 p. (2006; Zbl 1131.30325) Full Text: EuDML EMIS