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The purpose of this note is to study the following problem: which multi- valued generalized contractions are quasi-bounded with the quasi-norm strictly less than 1 ? As consequences, some surjectivity results are given.
Wydawca
Czasopismo
Rocznik
Tom
Strony
639--648
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Applied Mathematics Babes-Bolyai University Cluj-Napoca Kogalniceanu 1 400084, Cluj-Napoca, Romania, gabip@math.ubbcluj.ro
Bibliografia
- [1] F. Aldea, Surjectivity theorems for normcontraction operators, Mathematica 44 (2002), 129-136.
- [2] M. C. Anisiu, Quasibounded mappings and generalized contractions, Seminar on Fixed Point Theory, Preprint no. 3 (1983), 151-154.
- [3] J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers, Dordrecht, 2003.
- [4] J. -P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Basel, 1990.
- [5] L. B. Ciric, Fixed points for generalized multi-valued contractions, Mat. Vesn., N. Ser. 9(24) (1972), 265-272.
- [6] H. Covitz and S.B. Nadler jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
- [7] J. Dugundji and A. Granas, Fixed Point Theory, Springer Verlag, Berlin, 2003.
- [8] P. M. Fitzpatrick and W. V. Petryshyn, Fixed point theorems for multivalued noncompact acyclic mappings, Pacific J. Math. 54 (1974), mno. 2, 17-23.
- [9] S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I and II, Kluwer Academic Publishers, Dordrecht, 1997 and 1999.
- [10] R. Iannaci, The spectrum for nonlinear multi-valued maps via approximations, Boll. U. M. I., 15-B (1978), 527-545.
- [11] W. A. Kirk, B. Sims (editors), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publ., Dordrecht, 2001.
- [12] M. Martelli, Some results concerning multi-valued mappings defined in Banach spaces, Rend. Accad. Naz. Lincei LIV (1973), fasc. 6, 865-871.
- [13] M. Martelli and A. Vignoli, Some surjectivity results fo non-compact multi-valued maps, Rend. Accad. Sci. Fis. Mat. Napoli 41 (1974), 57-66.
- [14] S. Reich, Fixed point of contractive functions, Boll. U. M. I. 5 (1972), 26-42.
- [15] I. A. Rus, Generalized Contractions and Applications, Cluj Univ. Press, 2001.
- [16] I. A. Rus, Technique of the fixed point structures for multivalued mappings, Math. Japonica 38 (1993), 289-296.
- [17] I. A. Rus, Fixed point theorems for multivalued mappings in complete metric spaces, Math. Japonica 20 (1975), 21-24.
- [18] I. A. Rus, Normcontraction mappings outside a bounded subset, Itinerant Sem. On Functional Equations, Approx. and Convexity, 1986, 257-260.
- [19] I. A. Rus, A. Petruşel and A. Sîntămărian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003), 1947-1959.
- [20] I. A. Rus, A. Petruşel and G. Petruşel, Fixed Point Theory 1950-2000: Romanian Contributions, House of the Book of Science, Cluj-Napoca, 2002.
- [21] I. A. Rus, A. Petruşel and G. Petruşel, Fixed point theorems for set-valued Y -contractions, Fixed Point Theory and its Applications, Banach Center Publications, Vol. 77, Inst. Math., Polish Acad. Sci., Warszawa 2007, 227-237.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0035-0013