Geodesic
Existence and Ulam-Hyers stability results for coincidence problems
Mleşniţe, Oana1
1 Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu Street No.1, 400084, Cluj-Napoca, Romania
Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 2, p. 108-116.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.006.02.06
Classification : 47H10, 54H25
Keywords: metric space, coincidence problem, singlevalued contraction, vector-valued metric, fixed point, Ulam-Hyers stability.

Mleşniţe, Oana 1

1 Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu Street No.1, 400084, Cluj-Napoca, Romania 
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Mleşniţe, Oana. Existence and Ulam-Hyers stability results for coincidence problems. Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 2, p. 108-116. doi : 10.22436/jnsa.006.02.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.006.02.06/

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