Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 9 (2014), 167 -- 175

ULAM-HYERS STABILITY OF FIXED POINT EQUATIONS FOR MULTIVALUED OPERATORS ON KST SPACES

Liliana Guran Manciu

Abstract. In this paper we define the notions of Ulam-Hyers stability on KST spaces and cw-weakly Picard operator for the multivalued operators case in order to establish a relation between these.

2010 Mathematics Subject Classification: 47H10; 54H25; 54C60.
Keywords: Ulam-Hyers stability; w-distance, fixed point equation; Multivalued weakly Picard operator; Multivalued cw-weakly Picard operator.

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References

  1. J. Brzdek, D. Popa and B. Xu, The Hyers-Ulam stabililty of nonlinear recurrences, J. Math. Anal. Appl., 335(2007), 443-449. MR 2340333(2008f:39036). Zbl 1123.39022.

  2. J. Brzdek, D. Popa and B. Xu, Hyers-Ulam stabililty for linear equations of higher orders, Acta Math. Hungar., No. 1-2, 120 (2008), 1-8. MR 2431355 (2009e:39027). Zbl 1174.39012.

  3. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc., 215(1976), 241-251. MR 2625208. Zbl 0305.47029.

  4. A. Granas, J. Dugundji, Fixed Point Theory, Berlin, Springer-Verlag, 2003. MR 1987179(2004d:58012). Zbl 1025.47002.

  5. D.H. Hyers, The stability of homomorphism and related topics, Global Analysis - Analysis on Manifolds (Th.M. Rassians, ed.),Teubner-Texte Math., Teubner, Leipzig, 571983, 140-153. MR 0730609(86a:39004). Zbl 0517.22001.

  6. D.H. Hyers, G. Isac and Th.M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, Proc. Am. Math. Soc., No.2, 126(1998), 425-430. MR 1639801(99i:39035). Zbl 0894.39012.

  7. S.-M. Jung and K.-S. Lee, Hyers-Ulam-Rassias stability of linear differential equations of second order, J. Comput. Math. Optim., 3(2007), no. 3, 193-200. MR 2362444 (2008i:34008). Zbl 1130.26012.

  8. O. Kada, T. Suzuki and W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica, 44(1996), 381-391. MR 1416281(97j:49011). Zbl 0897.54029.

  9. N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., 141(1989), 177-188. MR 1004592 (90f:47086). Zbl 0688.54028.

  10. S.B. Nalder Jr., Multivalued contraction mappings, Pacific J. Math., 30(1969), 475-488. MR 0254828(40:8035). Zbl 0187.45002.

  11. T.P. Petru, A. Petruşel and J.-C. Yao, Ulam-Hyers stability for operatorial equations and inclusions via nonself operators, Taiwanese Journal of Mathematics, 15(2011), No. 5, pp. 2195-2212. MR 2880400. Zbl 1246.54049.

  12. A. Petruşel, Multivalued weakly Picard operators and applications, Scientiae Mathematicae Japonicae, 1(2004), 1-34. MR 2027745(2004j:47101). Zbl 1066.47058.

  13. A. Petruşel and I. A. Rus, Multivalued Picard and weakly Picard operators, Proceedings of the International Conference on Fixed Point Theory and Applications, Valencia (Spain), July 2003, 207-226; MR 2140219. Zbl 1091.47047.

  14. A. Petruşel and I. A. Rus, A. Sântămărian, Data dependence of the fixed point set of multivalued weakly Picard operators, Nonlinear Analysis, 52(2003), no. 8, 1947-1959. MR 1954261. Zbl 1055.47047.

  15. D. Popa, Hyers-Ulam stabililty of the linear recurrence with constant coefficients, Advances in Difference Equations, \bf 2(2005), 101-107. MR 2197125 (2006k:39009). Zbl 1095.39024.

  16. I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001. MR 1947742(2004f:54043). Zbl 0968.54029.

  17. I.A. Rus, Picard operators and applications, Scientiae Mathematicae Japonicae, 58(2003), 191-219.MR 1987831(2004m:47142). Zbl 1031.47035.

  18. I.A. Rus, Remarks on Ulam Stability of the operatorial equations, Fixed Point Theory, 10(2009), No. 2, 305-320. MR 2569004 (2010k:47128). Zbl 1204.47071.

  19. I.A. Rus, Ulam stability of ordinary differentioal equations, Studia Univ. Babeş-Bolyai Math., 54(2009), No. 4, 125-133. MR 2602351(2012b:34015). Zbl 1224.34165.

  20. I.A. Rus, A. Petruşel and G. Petruşel, Fixed Point Theory, Cluj University Press, 2008. MR MR2494238(2010a:47127). Zbl 1171.54034.

  21. N. Shioji, T. Suzuki and W. Takahashi, Contractive mappings, Kannan mappings and metric completeness, Proc. Amer. Math. Soc., 126(1998), 3117-3124. MR 1469434(99a:54023). Zbl 0955.54009.

  22. T. Suzuki and W. Takahashi, Fixed points theorems and characterizations of metric completeness, Topological Methods in Nonlinear Analysis, Journal of Juliusz Schauder Center, 8(1996), 371-382. MR 1483635(99c:54064). Zbl 0902.47050.



Liliana Guran Manciu
Department of Pharmaceutical Sciences,
Faculty of Medicine, Pharmacy and Dentistry,
Vasile Goldiş Western University of Arad,
Revoluţiei Avenue, no. 94-96, 310025, Arad, Romania.
E-mail: gliliana.math@gmail.com








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