Existence and Ulam-Hyers stability results for coincidence problems

Let X,Y be two nonempty sets and s,t:X→Y be two single-valued operators. By definition, a solution of the coincidence problem for s and t is a pair (x∗;y∗)∈X×Y such thats(x∗)=t(x∗)=y∗.It is well-known that a coincidence problem is, under appropriate conditions, equivalent to a fixed point problem for a single-valued operator generated by s and t. Using this approach, we will present some existence, uniqueness and Ulam - Hyers stability theorems for the coincidence problem mentioned above. Some examples illustrating the main results of the paper are also given.