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A multivalued version of Krasnoselskii’s theorem in generalized Banach spaces


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[1] G. Allaire and S.M. Kaber, Numerical Linear Algebra, Texts in Applied Mathematics, 55(2008), Springer, New York.10.1007/978-0-387-68918-0Search in Google Scholar

[2] A. Bucur, L. Guran, A. Petruşel, Fixed points for multivalued operators on a set endowed with vector-valued metrics and applications, Fixed Point Theory, 10(2009), No. 1, 19-34.Search in Google Scholar

[3] T.A. Burton, A fixed-point theorem of Krasnoselskii, Appl. Math. Letters, 11(1998), 85-88.10.1016/S0893-9659(97)00138-9Search in Google Scholar

[4] S. Carl, S. Heikkila, Fixed Point Theory in Ordered Sets and Applications, Springer, New York, 2011.10.1007/978-1-4419-7585-0Search in Google Scholar

[5] L. Collatz, Some applications of functional analysis to analysis, particularly to nonlinear integral equations, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis, 1970), Academic Press, New York, 1-43.10.1016/B978-0-12-576350-9.50004-7Search in Google Scholar

[6] H. Covitz, S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 8(1970), 5-11.10.1007/BF02771543Search in Google Scholar

[7] K. Deimling, Multivalued differential equations, W. de Gruyter, 1992.10.1515/9783110874228Search in Google Scholar

[8] A.-D. Filip, A. Petruşel, Fixed point theorems on spaces endowed with vector-valued metrics, FPTA, 2010(2010), Article ID 281381, 15 pp.10.1155/2010/281381Search in Google Scholar

[9] A. Granas, J. Dugundji, Fixed Point Theory, Springer, New York, 2003.10.1007/978-0-387-21593-8Search in Google Scholar

[10] D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publisher, Dordrecht, 1996.10.1007/978-1-4613-1281-9Search in Google Scholar

[11] W.A.J. Luxemburg, A.C. Zaanen, Riesz Spaces, North-Holland Publishing Company, Amsterdam, 1(1971).Search in Google Scholar

[12] I. Muntean, Capitole Speciale de Analiză Funcţională, Cluj-Napoca, 1990 (in Romanian).Search in Google Scholar

[13] I. Muntean, În legătură cu o teoremă de punct fix în spaţii local convexe, Rev. Roumaine Math. Pures Appl., 19(1974), 1105-1109 (in Russian).Search in Google Scholar

[14] S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 30(1969), 475-487.10.2140/pjm.1969.30.475Search in Google Scholar

[15] D. O’Regan, N. Shahzad, R.P. Agarwal, Fixed point theory for generalized contractive maps on spaces with vector-valued metrics, Fixed Point Theory and Applications, Nova Sci. Publ., New York, 6(2007), 143-149.Search in Google Scholar

[16] D. O’Regan, Fixed-point theory for the sum of two operators, Appl. Math. Let., 9(1996), 1-8.10.1016/0893-9659(95)00093-3Search in Google Scholar

[17] A.I. Perov, On the Cauchy problem for a system of ordinary differential equations, Priblizhen. Metody Reshen. Differ. Uravn., 2(1964), 115-134 (in Russian).Search in Google Scholar

[18] A.I. Perov, A.V. Kibenko, On a certain general method for investigation of boundary value problems, Izv. Akad. Nauk SSSR Ser. Mat., 30(1966), 249-264 (in Russian).Search in Google Scholar

[19] I.-R. Petre, A. Petruşel, Krasnoselskii’s theorem in generalized Banach spaces and applications, Electron. J. Qual. Theory Differ. Equ., 85(2012), 1-20.10.14232/ejqtde.2012.1.85Search in Google Scholar

[20] A. Petruşel, A generalization of Krasnoselskii’s fixed point theorem, Proc. Sci. Comm. Metting of ”Aurel Vlaicu” Univ. Arad, Vol. 14A(1996), 109-112.Search in Google Scholar

[21] A. Petruşel, Integral Inclusions. Fixed point approaches, Annales Soc. Math. Pol., Series I: Commentiones Mathematicae XL, 2000, 147-158.Search in Google Scholar

[22] A. Petruşel, Multivalued operators and fixed points, Pure Math. Appl., 11(2000), No. 2, 361-368.Search in Google Scholar

[23] A. Petruşel, Multivalued weakly Picard operators and applications, Sci. Math. Jap., 59(2004), No. 1, 169-202.Search in Google Scholar

[24] A. Petruşel, I.A. Rus, The theory of a metric fixed point theorem for multivalued operators, Fixed Point Theory and its Applications, Yokohama Publ., 2010, 167-176.10.1155/2010/178421Search in Google Scholar

[25] R. Precup, A. Viorel, Existence results for systems of nonlinear evolution equations, Intern. J. Pure Appl. Math., Vol. 47(2008), No. 2, 199-206.Search in Google Scholar

[26] R. Precup, A. Viorel, Existence results for systems of nonlinear evolution inclusions, Fixed Point Theory, 11(2010), No. 2, 337-346.Search in Google Scholar

[27] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.10.1007/978-94-015-9986-3Search in Google Scholar

[28] R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49(2009), No. 3-4, 703-708.Search in Google Scholar

[29] L. Rybinski, An application of the continuous selection theorem to the study of the fixed points of multivalued mappings, J. Math. Anal. Appl., 153(1990), 391-396.10.1016/0022-247X(90)90220-ASearch in Google Scholar

[30] I.A. Rus, A. Petruȩl, A. Sîntămărian, Data dependence of the fixed point set of multivalued weakly Picard operators, Nonlinear Anal., 52(2003), 1947-1959.10.1016/S0362-546X(02)00288-2Search in Google Scholar

[31] I.A. Rus, A. Petruşel, G. Petruşel, Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.Search in Google Scholar

[32] I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001.Search in Google Scholar

[33] I.A. Rus, Principles and Applications of the Fixed Point Theory, Dacia, Cluj-Napoca, 1979 (in Romanian).Search in Google Scholar

[34] I.A. Rus, Technique of the fixed point structures for multivalued mappings, Math. Japonica, 38(1993), 289-296.Search in Google Scholar

[35] R.S. Varga, Matrix Iterative Analysis, Vol. 27 of Springer Series in Computational Mathematics, Springer-Verlag, Berlin, 2000.10.1007/978-3-642-05156-2Search in Google Scholar

[36] A. Viorel, Contributions to the study of nonlinear evolution equations, Ph.D. Thesis, Babeş-Bolyai University Cluj-Napoca, 2011.Search in Google Scholar

[37] P.P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math., 48(1997), No. 4-6, 825-859.Search in Google Scholar

[38] A.C. Zaanen, Riesz Spaces, North-Holland Publishing Company, Amsterdam, 2(1983).Search in Google Scholar

[39] E. Zeidler, Nonlinear Functional Analysis, Vol. I, Fixed Point Theorems, Springer-Verlag, Berlin, 1993.Search in Google Scholar

[40] M. Zuluaga, On a fixed point theorem and application to a two-point boundary value problem, Comment. Math. Univ. Carolinae, 27(1986), 731-735.Search in Google Scholar

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