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Tytuł artykułu

A convergence theorem for some mean value fixed point iteration procedures

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Języki publikacji
EN
Abstrakty
EN
A general convergence theorem for the Ishikawa fixed point iteration procedure in a large class of quasi-contractive type operators is given. As particular cases, it contains convergence theorems for Picard, Krasnoselskij and Mann iterations, theorems which extend and generalize several results in the literature.
Wydawca
Rocznik
Strony
177--184
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
  • Department of Mathematics and Computer Science, North University of Baia, Mare Victoriei 76, 430122 Baia Mare, Romania
Bibliografia
  • [1] V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, Baia Mare, 2002.
  • [2] V. Berinde, Picard iteration converges faster than the Mann iteration for a class of quasi-contractive operators, Fixed Point Theory and Appl. 2 (2004), 97-105.
  • [3] V. Berinde, On the convergence of Mann iteration for a class of quasi contractive operators, (submitted).
  • [4] V. Berinde, On the convergence of Ishikawa iteration in the class of quasi contractive operators, Acta Math. Univ. Comenianae vol. LXXIII, 1 (2004), 119-126.
  • [5] F. 8. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math. 18, Pt. 2, Amer. Math. Soc., Providence, R. I., 1976.
  • [6] F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl. 20 (1967), 197-228
  • [7] S. K. Chatterjea, Fixed-point theorems, C.R. Acad. Bulgare Sci. 25 (1972), 727-730.
  • [8] Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Am. Math. Soc. 45 (1974) 267-273.
  • [9] C. W. Groetsch, A note on segmenting Mann iterates, J. Math. Anal. Appl. 40 (1972), 369-372.
  • [10] A. M. Harder and T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japonica 33 (1988), No. 5, 693-706.
  • [11] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44(1) (1974), 147-150.
  • [12] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71-76.
  • [13] R. Kannan, Some results on fixed points. III, Fund. Math. 70 (1971), 169-177.
  • [14] R. Kannan, Construction of fixed points of a class of nonlinear mappings, J. Math. Anal. Appl. 41 (1973), 430-438.
  • [15] W. A. Kirk and B. Sims, Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, 2001.
  • [16] M. A. Krasnoselskij, Two remarks on the method of successive approximations, (Russian ) Uspehi Mat. Nauk. 10 (1955), no. 1 (63), 123-127.
  • [17] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 44 (1953), 506-510.
  • [18] M. O. Osilike, Stability results for fixed point iteration procedures, J. Nigerian Math. Soc. 14/15 (1995/96), 17-29.
  • [19] M. O. Osilike, Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings, Indian J. Pure Appl. Math. 30 (12) (1999), 1229-1234.
  • [20] B . E. Rhoades, Fixed point iterations using infinite matrices, Trans. Amer. Math. Soc. 196 (1974), 161-176.
  • [21] B. E. Rhoades, Comments on two fixed point iteration methods, J. Math. Anal. Appl. 56 (1976), No. 2, 741-750.
  • [22] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.
  • [23] B. E. Rhoades, Contractive definitions revisited, Contemporary Math. 21 (1983), 189-205.
  • [24] B. E. Rhoades, Contractive definitions and continuity, Contemporary Math., 72 (1988 ), 233-245.
  • [25] B. E. Rhoades, Some fixed point iteration procedures, Int. J. Math. Math. Sci. 14 (1991), No. 1, 1-16.
  • [26] I. A. Rus, Principles and Applications of the Fixed Po int. Theory, (Romanian) Editura Dacia, Cluj-Napoca, 1979.
  • [27] I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001.
  • [28] T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math. (Basel), 23 (1972), 292-298.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0012-0019
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