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Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces

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Abstrakty
EN
In this paper, we establish some fixed point theorems for Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces and deduce similar other results on Mann and Ishikawa iterations as special cases. Our results improve a multitude of recent results in the fixed point theory especially the result of Ciric [5].
Rocznik
Tom
Strony
29--38
Opis fizyczny
Bibliogr. 29 poz.
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autor
Bibliografia
  • [1] Agarwal R.P., Meehan M., Oregan D., Fixed Point Theory and Applications, Cambridge University Press, 2001.
  • [2] Berinde V., Iterative approximation of fixed points for pseudo-contractive operators, Seminar on Fixed Point Theory, 3(2001), 210-216.
  • [3] Berinde V., Iterative Approximation of Fixed Points, Editura Efemeride. 2002
  • [4] Ciric L.B., Quasi-contractions in Banach spaces, Publ. Inst. Math., (Beograd) (N.S), 21(35)(1977), 11-18.
  • [5] Ciric L.B., Fixed point theorems in Banach spaces, Publ. Inst. Math., (Beograd), 47(61)(1990), 85-87.
  • [6] Ciric L.B., Fixed Point Theory. Contraction Mapping Principle, FME Press, Beograd 2003.
  • [7] Edelstein M., A remark on a theorem of M.A Krasnoselkij, Amer. Math., Monthly 73(1966), 509-510.
  • [8] Goebel K., Kirk W., Shimi T., A fixed point theorem in uniformly convex spaces, Bull. U.M.E, 4(7)(1973), 67-75.
  • [9] Imoru C.O., Akinbo G., Bosede A.O., On the fixed points for weak compatible type and parametrically ϕ(ε,δ,α)-contraction mappings, Math. Sci. Res. Journal, 10(10)(2006), 259-267.
  • [10] Ishikawa S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44(1974), 147-150.
  • [11] Mann W.R., Mean value iteration, Proc. Amer. Math. Soc., 4(1953), 506-510.
  • [12] Mutangadura S.A., Chidume C.E., An example on the Mann iteration method for Lipschitz pseudocontraction, Proc. Amer. Math. Soc., 129(2001), 2359-2363.
  • [13] Noor M.A., General variational inequalities, Appl. Math. Letters, 1(1988), 119-121.
  • [14] Noor M.A., New approximations schemes for general variational inequalities, Math. Anal. Appl., 251(2000), 217-299.
  • [15] Noor M.A., Some new developments in general variational inequalities, Appl. Math. Computation, 152(2004), 199-277.
  • [16] Noor M.A., Noor K.I., Rassias T.M., Some aspects of variational inequalities, J. Comput. Appl. Math., 47(1993), 493-512.
  • [17] Osilike M.O., Some stability results for fixed point iteration procedures, J. Nigerian Math. Soc., 14/15(1995), 17-29.
  • [18] Owojori O.O., Imoru C.O., On a general Ishikawa fixed point iteration process for continuous hemicontractive maps in Hilbert spaces, Advanced Studies in Contemporary Mathematics, 4(1)(2001), 1-15.
  • [19] Owojori O.O., On generalized fixed point iterations for asymptotically nonexpansive maps in arbitrary Banach spaces, Proceedings Jangjeon Mathematical Society, 6(1)(2003), 49-58.
  • [20] Park J.A., Mann-iteration for strictly pseudocontractive maps, J. Korean Math. Soc., 31(1994), 333-337.
  • [21] Rhoades B.E., Fixed point theorems and stability results for fixed point iteration procedures, Indian J. Pure Appl. Math., 21(1)(1990), 1-9.
  • [22] Rhoades B.E., Some fixed point iteration procedures, Internat. J. Math. And Math. Sci., 14(1)(1991), 1-16.
  • [23] Rus I.A., Basic problems of the metric fixed point theory revisited (11), Stud. Univ. Babes-Bolyal, 36(1991), 81-99.
  • [24] Rus I.A., Generalized Contractions and Applications, Cluj-Napoca 2001.
  • [25] Rus I.A., Petrusel A., Petrusel G., Fixed Point Theory, 1950-2000, Romanian Contributions, House of the Book of Science, Cluj-Napoca 2002.
  • [26] Weng X.L., Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc., 113(1991), 727-731.
  • [27] Xu B., Noor M.A., Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, Journal of Mathematical Analysis and Applications, 267(2002), 444-453.
  • [28] Zamfirescu T., Fix point theorems in metric spaces, Arch. Math., 23(1972), 292-298.
  • [29] Zeidler E., Nonlinear Functional Analysis and its Applications:Fixed Point Theorems, Springer Verlag, New York, Inc. 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP3-0002-0050
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