Question Find the largest possible domain contained in $\Im (z)>0$ such that $s (z)$ is injective. My ideas Let, $z$, $w\in \mathbb {C}$ be such that $$s (z)=s (w) $$ $$\frac { (2z+i)^2} {4z^2-1}=\frac { (2w+i)^2} {4w^2-1} $$ which on simplification gives $$ (4zw+1) (w-z)=0 $$ So, we need a domain …

In mathematics, an injective function (also known as injection, or one-to-one function[1]) is a function f that maps distinct elements of its domain to distinct elements of its codomain; that is, x1 ≠ x2 implies f(x1) ≠ f(x2) (equivalently by contraposition, f(x1) = f(x2) implies x1 = x2). In other …

Functions can be injections (one-to-one functions), surjections (onto functions) or bijections (both one-to-one and onto). Informally, an injection has each output mapped to by at most one input, a surjection includes the entire possible range in the output, and a bijection has both conditions be …

We typically think of a function as taking objects from one set, , A, doing “stuff” and turning them into elements from another set . B With this in mind, it is quite natural to ask whether or not we can reverse this process; take our result and turn it back into our original object. That is, “when …

such an example was not known at that time. In 1991, when told by P. Duren, he pres tion to the theory of analytic functions o nd conjectures in planar harm ns harmo omplex plane, Cambridge tracts in mathematics, x analysis in several esbe several complex variables, AMS Chelsea Pub for hi her d …

In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to …