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2008 | 6 | 4 | 610-621
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Some results on multi-valued weakly jungck mappings in b-metric space

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
4
Strony
610-621
Opis fizyczny
Daty
wydano
2008-12-01
online
2008-10-08
Twórcy
Bibliografia
  • [1] Agarwal R.P., Meehan M., O’Regan D., Fixed point theory and applications, Cambridge University Press, Cambridge, 2001
  • [2] Banach S., Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math., 1922, 3, 133–181 (in French)
  • [3] Berinde V., A priori and a posteriori error estimates for a class of ϕ-contractions, Bulletins for Applied & Computing Math., 1999, 183–192
  • [4] Berinde V., Iterative approximation of fixed points, Editura Efemeride, Baia Mare, 2002
  • [5] Berinde V., On the approximation of fixed points of weak ϕ-contractive operators, Fixed Point Theory, 2003, 4, 131–142
  • [6] Berinde V., On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 2003, 19, 7–22
  • [7] Berinde V., Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 2004, 9, 43–53
  • [8] Berinde M., Berinde V., On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl., 2007, 326, 772–782 http://dx.doi.org/10.1016/j.jmaa.2006.03.016
  • [9] Boyd D.W., Wong J.S.W., On nonlinear contractions, Proc. Amer. Math. Soc., 1969, 20, 458–464 http://dx.doi.org/10.2307/2035677
  • [10] Browder F., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., 1965, 54, 1041–1044 http://dx.doi.org/10.1073/pnas.54.4.1041
  • [11] Czerwik S., Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1993, 1, 5–11
  • [12] Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 1998, 46, 263–276
  • [13] Ciric L.B., Fixed point theory, contraction mapping principle, FME Press, Beograd, 2003
  • [14] Ciric L.B., Ume J.S., Common fixed point theorems for multi-valued non-self mappings, Publ. Math. Debrecen, 2002, 60, 359–371
  • [15] Ciric L.B., Ume J.S., On the convergence of Ishikawa iterates to a common fixed point of multi-valued mappings, Demonstratio Math., 2003, 36, 951–956
  • [16] Daffer P.Z., Kaneko H., Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl., 1995, 192, 655–666 http://dx.doi.org/10.1006/jmaa.1995.1194
  • [17] Geraghty M.A., On contractive mappings, Proc. Amer. Math. Soc., 1973, 40, 604–608 http://dx.doi.org/10.2307/2039421
  • [18] Goffman C., Pedrick G., First course in functional analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1965
  • [19] Itoh S., Multivalued generalized contractions and fixed point theorems, Comment. Math. Univ. Carolinae, 1977, 18, 247–258
  • [20] Joshi M.C., Bose R.K., Some topics in nonlinear functional analysis, John Wiley & Sons, Inc., New York, 1985
  • [21] Kaneko H., A general principle for fixed points of contractive multivalued mappings, Math. Japon., 1986, 31, 407–411
  • [22] Kaneko H., Generalized contractive multivalued mappings and their fixed points, Math. Japon., 1988, 33, 57–64
  • [23] Khamsi M.A., Kirk W.A., An introduction to metric spaces and fixed point theory, Wiley-Interscience, New York, 2001
  • [24] Kubiaczyk I., Ali N.M., On the convergence of the Ishikawa iterates to a common fixed point for a pair of multi-valued mappings, Acta Math. Hungar., 1997, 75, 253–257 http://dx.doi.org/10.1023/A:1006555406715
  • [25] Lim T.C., On fixed point stability for set-valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl., 1985, 110, 436–441 http://dx.doi.org/10.1016/0022-247X(85)90306-3
  • [26] Markins J.T., A fixed point theorem for set-valued mappings, Bull. Amer. Math. Soc., 1968, 74, 639–640 http://dx.doi.org/10.1090/S0002-9904-1968-11971-8
  • [27] Mizoguchi M., Takahashi W., Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl., 1989, 141, 177–188 http://dx.doi.org/10.1016/0022-247X(89)90214-X
  • [28] Nadler S.B., Multi-valued contraction mappings, Pacific J. Math., 1969, 30, 475–488
  • [29] Olatinwo M.O., A generalization of some results on multi-valued weakly Picard mappings in b-metric space, preprint
  • [30] Picard E., Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J.Math. Pures et Appl., 1890, 6, 145–210 (in French)
  • [31] Rhoades B.E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 1977, 226, 257–290 http://dx.doi.org/10.2307/1997954
  • [32] Rhoades B.E., A fixed point theorem for a multivalued non-self mapping, Comment. Math. Univ. Carolin., 1996, 37, 401–404
  • [33] Rhoades B.E., Watson B., Fixed points for set-valued mappings on metric spaces, Math. Japon., 1990, 35, 735–743
  • [34] Rus I.A., Fixed point theorems for multi-valued mappings in complete metric spaces, Math. Japon., 1975, 20, 21–24
  • [35] Rus I.A., Generalized contractions and applications, Cluj University Press, Cluj Napoca, 2001
  • [36] Rus I.A., Petrusel A., Petrusel G., Fixed point theory: 1950-2000, Romanian Contributions, House of the Book of Science, Cluj Napoca, 2002
  • [37] Singh S.L., Bhatnagar C., Hashim A.M., Round-off stability of Picard iterative procedure for multivalued operators, Nonlinear Anal. Forum, 2005, 10, 13–19
  • [38] Zeidler E., Nonlinear functional analysis and its applications-fixed point theorems, Springer-Verlag, New York, Inc., 1986
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0047-3
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