Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2010 | 8 | 2 | 367-377
Tytuł artykułu

Multivalued fractals in b-metric spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.
Opis fizyczny
  • [1] Andres J., Fišer J., Metric and topological multivalued fractals, Int. J. Bifurc. Chaos Appl. Sci. Engn., 2004, 14, 1277–1289
  • [2] Andres J., Fišer J., Gabor G., Leśniak K., Multivalued fractals, Chaos Solitons & Fractals, 2005, 24, 665–700
  • [3] Bakhtin I.A., The contraction mapping principle in almost metric spaces, Funct. Anal, Gos. Ped. Inst. Unianowsk, 1989, 30, 26–37
  • [4] Barnsley M.F, Fractals Everywhere, Academic Press, Boston, 1988
  • [5] Berinde V, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, 1993, 3–9
  • [6] Berinde V, Sequences of operators and fixed points in quasimetric spaces, Studia Univ. Babeş-Bolyai, Math., 1996, 16,23–27
  • [7] Blumenthal L.M., Theory and Applications of Distance Geometry, Oxford Univ. Press, Oxford, 1953
  • [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] Bourbaki N., Topologie générale, Herman, Paris, 1974
  • [10] Browder FE., On the convergence of successive approximations for nonlinear functional equations, Indag. Math., 1968,30,27–35
  • [11] Chifu C, Petruşel A., Multivalued fractals and generalized multivalued contractions, Chaos Solitons & Fractals, 2008,36,203–210
  • [12] Covitz H., Nadler S.B. jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 1970, 8, 5–11
  • [13] Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 1998, 46, 263–276
  • [14] El Naschie M.S., Iterated function systems and the two-slit experiment of quantum mechanics, Chaos Solitons & Fractals, 1994, 4, 1965–1968
  • [15] Fréchet M., Les espaces abstraits, Gauthier-Villars, Paris, 1928
  • [16] Heinonen J., Lectures on Analysis on Metric Spaces, Springer Berlin, 2001
  • [17] Hu S., Papageorgiou N.S., Handbook of Multivalued Analysis, Vol. I, II, Kluwer Acad. Publ., Dordrecht, 1997, 1999
  • [18] Hutchinson J.E., Fractals and self-similarity, Indiana Univ. Math. J., 1981, 30, 713–747
  • [19] Jachymski J., Matkowski J., Światkowski T., Nonlinear contractions on semimetric spaces, J. Appl. Anal., 1995, 1, 125–134
  • [20] Kirk W.A., Sims B. (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publ., Dordrecht, 2001
  • [21] Llorens-Fuster E., Petruşel A., Yao J.C., Iterated function systems and well-posedness, Chaos Solitons & Fractals, 2009, 41, 1561–1568
  • [22] Meir A., Keeler E., A theorem on contraction mappings, J. Math. Anal. Appl., 1969, 28, 326–329
  • [23] Nadler S.B. Jr., Multivalued contraction mappings, Pacific J. Math., 1969, 30, 475–488
  • [24] Păcurar (Berinde) M., Iterative methods for fixed point approximation, Ph.D. thesis, Babeş-Bolyai University Cluj-Napoca, Romania, 2009
  • [25] Păcurar (Berinde) M., A fixed point result for ϕ-contractions on b-metric spaces without the boundedness assumption, preprint
  • [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
  • [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
  • [28] Rhoades B.E., Some theorems on weakly contractive maps, Nonlinear Anal., 2001, 47, 2683–2693
  • [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
  • [30] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001
  • [31] Rus I.A., Picard operators and applications, Sci. Math. Japon., 2003, 58, 191–219
  • [32] Rus I.A., Strict fixed point theory, Fixed Point Theory, 2003, 4, 177–183
  • [33] Rus I.A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 2008, 9, 541–559
  • [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
  • [35] Singh S.L., Prasad B., Kumar A., Fractals via iterated functions and multifunctions, Chaos Solitons & Fractals, 2009, 39, 1224–1231
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.