Existence and Ulam-Hyers stability results for coincidence problems


Oana Mleşniţe - Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu Street No.1, 400084, Cluj-Napoca, Romania.


Let \(X, Y\) be two nonempty sets and \(s, t : X \rightarrow Y\) be two single-valued operators. By definition, a solution of the coincidence problem for s and \(t\) is a pair \((x^*; y^*) \in X \times Y\) such that \[s(x^*) = t(x^*) = y^*.\] 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.