Existence and Ulam-Hyers stability results for coincidence problems
- 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.
- metric space
- coincidence problem
- singlevalued contraction
- vector-valued metric
- fixed point
- Ulam-Hyers stability.
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