Multivalued fractals in b-metric spaces

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1. [1] Andres J., Fišer J., Metric and topological multivalued fractals, Int. J. Bifurc. Chaos Appl. Sci. Engn., 2004, 14, 1277–1289 http://dx.doi.org/10.1142/S021812740400979X Zbl1057.28003
2. [2] Andres J., Fišer J., Gabor G., Leśniak K., Multivalued fractals, Chaos Solitons & Fractals, 2005, 24, 665–700 http://dx.doi.org/10.1016/j.chaos.2004.09.029 Zbl1077.28002
3. [3] Bakhtin I.A., The contraction mapping principle in almost metric spaces, Funct. Anal, Gos. Ped. Inst. Unianowsk, 1989, 30, 26–37 Zbl0748.47048
4. [4] Barnsley M.F, Fractals Everywhere, Academic Press, Boston, 1988 
5. [5] Berinde V, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, 1993, 3–9 
6. [6] Berinde V, Sequences of operators and fixed points in quasimetric spaces, Studia Univ. Babeş-Bolyai, Math., 1996, 16,23–27 Zbl1005.54501
7. [7] Blumenthal L.M., Theory and Applications of Distance Geometry, Oxford Univ. Press, Oxford, 1953 
8. [8] Boriceanu M., Petruşel A., Rus I.A., Fixed point theorems for some multivalued generalized contractions in b-metric spaces, Internat. J. Math. Statistics, 2010, 6, 65–76 
9. [9] Bourbaki N., Topologie générale, Herman, Paris, 1974 
10. [10] Browder FE., On the convergence of successive approximations for nonlinear functional equations, Indag. Math., 1968,30,27–35 Zbl0155.19401
11. [11] Chifu C, Petruşel A., Multivalued fractals and generalized multivalued contractions, Chaos Solitons & Fractals, 2008,36,203–210 http://dx.doi.org/10.1016/j.chaos.2006.06.027 Zbl1131.28005
12. [12] Covitz H., Nadler S.B. jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 1970, 8, 5–11 http://dx.doi.org/10.1007/BF02771543 Zbl0192.59802
13. [13] Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 1998, 46, 263–276 Zbl0920.47050
14. [14] El Naschie M.S., Iterated function systems and the two-slit experiment of quantum mechanics, Chaos Solitons & Fractals, 1994, 4, 1965–1968 http://dx.doi.org/10.1016/0960-0779(94)90011-6 
15. [15] Fréchet M., Les espaces abstraits, Gauthier-Villars, Paris, 1928 
16. [16] Heinonen J., Lectures on Analysis on Metric Spaces, Springer Berlin, 2001 
17. [17] Hu S., Papageorgiou N.S., Handbook of Multivalued Analysis, Vol. I, II, Kluwer Acad. Publ., Dordrecht, 1997, 1999 Zbl0887.47001
18. [18] Hutchinson J.E., Fractals and self-similarity, Indiana Univ. Math. J., 1981, 30, 713–747 http://dx.doi.org/10.1512/iumj.1981.30.30055 Zbl0598.28011
19. [19] Jachymski J., Matkowski J., Światkowski T., Nonlinear contractions on semimetric spaces, J. Appl. Anal., 1995, 1, 125–134 http://dx.doi.org/10.1515/JAA.1995.125 Zbl1295.54055
20. [20] Kirk W.A., Sims B. (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publ., Dordrecht, 2001 Zbl0970.54001
21. [21] Llorens-Fuster E., Petruşel A., Yao J.C., Iterated function systems and well-posedness, Chaos Solitons & Fractals, 2009, 41, 1561–1568 http://dx.doi.org/10.1016/j.chaos.2008.06.019 Zbl1198.52014
22. [22] Meir A., Keeler E., A theorem on contraction mappings, J. Math. Anal. Appl., 1969, 28, 326–329 http://dx.doi.org/10.1016/0022-247X(69)90031-6 
23. [23] Nadler S.B. Jr., Multivalued contraction mappings, Pacific J. Math., 1969, 30, 475–488 Zbl0187.45002
24. [24] Păcurar (Berinde) M., Iterative methods for fixed point approximation, Ph.D. thesis, Babeş-Bolyai University Cluj-Napoca, Romania, 2009 
25. [25] Păcurar (Berinde) M., A fixed point result for ϕ-contractions on b-metric spaces without the boundedness assumption, preprint 
26. [26] Petruşel A., Rus I.A., Well-posedness of the fixed point problem for multivalued operators, Applied Analysis and Differential Equations (Cârjă O., Vrabie I.I. (Eds.) World Scientific 2007, 295–306 Zbl1169.47037
27. [27] Petruşel A., Rus I.A., Yao J.C., Well-posedness in the generalized sense of the fixed point problems for multivalued operators, Taiwanese J. Math., 2007, 11, 903–914 Zbl1149.54022
28. [28] Rhoades B.E., Some theorems on weakly contractive maps, Nonlinear Anal., 2001, 47, 2683–2693 http://dx.doi.org/10.1016/S0362-546X(01)00388-1 Zbl1042.47521
29. [29] Rus I.A., Petruşel A., Sîntămărian A., Data dependence of the fixed points set of some multivalued weakly Picard operators, Nonlinear Anal., 2003, 52, 1947–1959 http://dx.doi.org/10.1016/S0362-546X(02)00288-2 
30. [30] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001 
31. [31] Rus I.A., Picard operators and applications, Sci. Math. Japon., 2003, 58, 191–219 
32. [32] Rus I.A., Strict fixed point theory, Fixed Point Theory, 2003, 4, 177–183 Zbl1070.47519
33. [33] Rus I.A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 2008, 9, 541–559 Zbl1172.54030
34. [34] Singh S.L., Bhatnagar C., Mishra S.N., Stability of iterative procedures for multivalued maps in metric spaces, Demonstratio Math., 2005, 37, 905–916 Zbl1100.47056
35. [35] Singh S.L., Prasad B., Kumar A., Fractals via iterated functions and multifunctions, Chaos Solitons & Fractals, 2009, 39, 1224–1231 http://dx.doi.org/10.1016/j.chaos.2007.06.014 Zbl1197.28004