We introduce the concept of a subordination, which is dual to the well-known concept of a precontact on a Boolean algebra. We develop a full categorical duality between Boolean algebras with a subordination and Stone spaces with a closed relation, thus generalizing the results of [14]. We introduce the concept of an irreducible equivalence relation, and that of a Gleason space, which is a pair ...

In this present investigation, we obtain some results for certain second order linear differential subordination. We also discuss some applications of our results.

In this paper, we consider functions analytic in the unit disk that are subordinate to of same type defined by certain differential subordinations. We prove several sharp majorization theorems and a product theorem.