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2016 | Nr 56 | 167--184
Tytuł artykułu

New stability results of picard iteration for contractive type mappings

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Języki publikacji
EN
Abstrakty
EN
There exists several concepts of stability for fixed point iterative methods in literature. The aim of this paper is to compare two such concepts, namely one due to Harder and the second one due to Rus, in the class of contractive mappings.
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Rocznik
Tom
Strony
167--184
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
  • Technical University of Cluj-Napoca, North University Center from Baia Mare, Department of Mathematics and Informatics, Str Victoriei 76, 430122, Baia Mare, Romania , ioana.daraban@yahoo.com
Bibliografia
  • [1] Babu G.V.R., Sandhya M.L., Kameswari M.V.R., A note on a fixed point theorem of Berinde on weak contractions, Carpathian J. Math., 24(1) (2008), 8-12.
  • [2] Banach S., Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math., 3(1922), 133-181.
  • [3] Berinde V., Approximating common fixed points of noncommuting almost contractions in metric spaces, Fixed Point Theory, 11(2) (2010), 179-188.
  • [4] Berinde V., Approximation fixed points of weak contractions using Picard iteration, Nonlinear Analysis Forum, 9(1) (2004), 43-53.
  • [5] Berinde V., Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun., 15(1) (2010), 229-241.
  • [6] Berinde V., Iterative Approximation of Fixed Points, Springer Verlag, Lectures Notes in Mathematics, 2007.
  • [7] Berinde V., On the stability of fixed point iteration procedures, Bul. Stiint. Univ. Baia Mare, Fasc.Mat.-Inf., vol. XVIII (2002), No. 1, 7-12.
  • [8] Chatterjea S.K., Fixed point theorems, C.R. Acad. Bulgare Sci., 25(1972), 727-730.
  • [9] Eirola T., Nevanlinna O., Pilyugin S.Yu., Limit shadowing property, Numer. Funct. Analysis and Opt., 18(1997), 75-92.
  • [10] Harder A.M., Fixed point theory and stability results for fixed point iteration procedures, Ph.D. thesis, University of Missouri-Rolla, Missouri, 1987.
  • [11] Harder A.M., Hicks T.L., A stable iteration procedure for nonexpansive mappings, Math. Japon., 33(1988), 687-692.
  • [12] Harder A.M., Hicks T.L., Stability results for fixed point iteration procedures, Math. Japon., 33(1988), 693-706.
  • [13] Kannan R., Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), 71-76.
  • [14] Osilike M.O., A stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math., 27(1) (1996), 25-34.
  • [15] Osilike M.O., Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math., 28(9) (1997), 1251-1265.
  • [16] Osilike M.O., Stability results for fixed point iteration procedure, J. Nigerian Math. Soc., 14(1995), 17-29.
  • [17] Osilike M.O., Stable iteration procedures for strong pseudo-contractions and nonlinear operator equations of the accretive type, Journal of Mathematical Analysis and Applications, 204(1996), 677-692.
  • [18] Osilike M.O., Udomene A., 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.
  • [19] Ostrowski A.M., The round-off stability of iterations, Z. Angew. Math. Mech., 47(1) (1967), 77-81.
  • [20] Păcurar M., Iterative methods for fixed point approximations, Risoprint, Cluj-Napoca, 2009.
  • [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., Fixed point theorems and stability results for fixed point iteration procedures II, Indian J. Pure Appl. Math., 24(11) (1993), 691-703.
  • [23] Rus I.A., An abstract point of view on iterative approximation of fixed points: impact on the theory of fixed point equations, Fixed Point Theory, 13(1) (2012), 179-192.
  • [24] Rus I.A., Generalized contractions and applications, Cluj University Press, Cluj-Napoca, 2001.
  • [25] Rus I.A., Principles and applications of the fixed point theory, Editura Dacia, Cluj-Napoca, 1979.
  • [26] Timiş I., On the weak stability of Picard iteration for some contractive type mappings, Annals of the University of Craiova - Mathematics and Computer Science Series, 37(2)(2010), 106-114.
  • [27] Zamfirescu T., Fixed point theorems in metric spaces, Arch. Math., 23(1972), 292-298.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-cef8b11e-5543-4476-8182-a931f76a70f4
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