Inequalities for Meromorphic Functions Not Vanishing Outside the Disk

Abstract

For a polynomial having all zeros inside a unit disk, Dubinin [Applications of the Schwarz lemma to inequalities for entire functions with constraints on zeros, Journal of Mathematical Sciences, 143 (2007), 3069-3076] proved:Various refinements and generalizations of this result were proved, we prove some results which include the results of Wali and Shah [Some applications of Dubinin's lemma to rational functions with prescribed poles, J. Math. Anal. Appl., 450, (2017), 769-779] besides the above inequality due to Dubinin as special cases.

Some Turan-type inequalities for a class of rational functions with prescribed poles

“…By involving some coefficients of the polynomial P (z), Mir et al [8] generalized as well as improved inequality (1.4) by proving the following result.…”