Existence and UlamHyers stability results for coincidence problems
Authors
Oana Mleşniţe
 Department of Mathematics, BabeşBolyai University ClujNapoca, Kogălniceanu Street No.1, 400084, ClujNapoca, Romania.
Abstract
Let \(X, Y\) be two nonempty sets and \(s, t : X \rightarrow Y\) be two singlevalued 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 wellknown that a coincidence problem is, under appropriate conditions, equivalent to a fixed point
problem for a singlevalued 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.
Keywords
 metric space
 coincidence problem
 singlevalued contraction
 vectorvalued metric
 fixed point
 UlamHyers stability.
MSC
References

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