Non-autonomous Differential Subordinations Related to a Sector

摘要

Let be a complex valued function defined in the unit disc and let be a function analytic in with and in . In this article, we determine the largest constants and conditions on such that for given and , the non-autonomous differential subordination implies in . Here the symbol ` ' stands for subordination. Almost all the previously known results on differential subordination concerning a sector follow as particular cases of our results.