Geodesic
Ulam-Hyers stability for coupled fixed points of contractive type operators
Urs, Cristina1
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. 124-136.

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

In this paper, we present existence, uniqueness and Ulam-Hyers stability results for the coupled fixed points of a pair of contractive type singlevalued and respectively multivalued operators on complete metric spaces. The approach is based on Perov type fixed point theorem for contractions in spaces endowed with vector- valued metrics.
DOI : 10.22436/jnsa.006.02.08
Classification : 47H10, 54H25
Keywords: metric space, coupled fixed point, singlevalued operator, vector-valued metric, Perov type contraction.

Urs, Cristina 1

1 Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu Street no. 1, 400084, Cluj-Napoca, Romania 
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Urs, Cristina. Ulam-Hyers stability for coupled fixed points of contractive type operators. Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 2, p. 124-136. doi : 10.22436/jnsa.006.02.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.006.02.08/

[1] Allaire, G.; Kaber, S. M. Numerical Linear Algebra, Texts in Applied Mathematics, vol. 55, Springer, New York, 2008

[2] Bota, M.; Petrusel, A. Ulam-Hyers stability for operatorial equations, Analls of the Alexandru Ioan Cuza University Iasi, Volume 57 (2011), pp. 65-74

[3] Bucur, A.; Guran, L.; A. Petrusel Fixed points for multivalued operators on a set endowed with vector-valued metrics and applications, Fixed Point Theory, Volume 10 (2009), pp. 19-34

[4] Filip, A. D.; Petrusel, A. Fixed point theorems on spaces endowed with vector-valued metrics, Fixed Point Theory and Applications, Article ID 281381, Volume 2010 (2009), pp. 1-15

[5] Filip, A. D.; A. Petrusel Fixed point theorems on spaces endowed with vector-valued metrics, Fixed Point Theory and Applications, Article ID 281381, Volume 2010 (2009), pp. 1-15

[6] Bhaskar, T. Gnana; Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., Volume 65 (2006), pp. 1379-1393

[7] Guo, D.; Lakshmikantham, V. Coupled fixed points of nonlinear operators with applications , Nonlinear Anal., Volume 11 (1987), pp. 623-632

[8] Guo, D.; Cho, Y. J.; Zhu, J. Partial Ordering Methods in Nonlinear Problems, Nova Science Publishers Inc., Hauppauge, NY, 2004

[9] Hong, S. Fixed points for mixed monotone multivalued operators in Banach spaces with applications, J. Math. Anal. Appl., Volume 337 (2008), pp. 333-342

[10] Lakshmikantham, V.; Ćirić, L. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. , Volume 70 (2009), pp. 4341-4349

[11] A. I. Perov On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Differ. Uvavn, Volume 2 (1964), pp. 115-134

[12] Petru, P. T.; Petrusel, A.; Yao, J. C. Ulam-Hyers stability for operatorial equations and inclusions via nonself operators, Taiwanese J. Math., Volume 15 (2011), pp. 2195-2212

[13] Petrusel, A. Multivalued weakly Picard operators and applications, Sci. Math. Japon, Volume 59 (2004), pp. 169-202

[14] R. Precup The role of matrices that are convergent to zero in the study of semilinear operator systems, Math. Comput. Modell, Volume 49 (2009), pp. 703-708

[15] Rus, I. A. Principles, Applications of the Fixed Point Theory, Dacia, Cluj-Napoca, 1979

[16] Rus, I. A. Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, Volume 10 (2009), pp. 305-320

[17] Rus, M. D. The method of monotone iterations for mixed monotone operators, Ph. D. Thesis, Universitatea Babes-Bolyai, Cluj-Napoca, 2010

[18] Varga, R. S. Matrix Iterative Analysis, Springer Series in Computational Mathematics, Vol. 27, Springer, Berlin, 2000

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