Existence and Ulam-Hyers stability results for coincidence problems
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Authors
Oana Mleşniţe
- Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu Street No.1, 400084, Cluj-Napoca, Romania.
Abstract
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.
Share and Cite
ISRP Style
Oana Mleşniţe, Existence and Ulam-Hyers stability results for coincidence problems, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 2, 108--116
AMA Style
Mleşniţe Oana, Existence and Ulam-Hyers stability results for coincidence problems. J. Nonlinear Sci. Appl. (2013); 6(2):108--116
Chicago/Turabian Style
Mleşniţe, Oana. "Existence and Ulam-Hyers stability results for coincidence problems." Journal of Nonlinear Sciences and Applications, 6, no. 2 (2013): 108--116
Keywords
- metric space
- coincidence problem
- singlevalued contraction
- vector-valued metric
- fixed point
- Ulam-Hyers stability.
MSC
References
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