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2013 | 11 | 3 | 552-560
Tytuł artykułu

Fixed points for cyclic orbital generalized contractions on complete metric spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir-Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and Agrawal.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
3
Strony
552-560
Opis fizyczny
Daty
wydano
2013-03-01
online
2012-12-22
Twórcy
  • Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022, Valencia, Spain, sromague@mat.upv.es
autor
  • Department of Mathematics and Computer Science, Çankaya University, 06530, Yuzuncuyil, Ankara, Turkey, kenan@cankaya.edu.tr
Bibliografia
  • [1] Al-Thagafi M.A., Shahzad N., Convergence and existence results for best proximity points, Nonlinear Anal., 2009, 70(10), 3665–3671 http://dx.doi.org/10.1016/j.na.2008.07.022[WoS][Crossref]
  • [2] Anuradha J., Veeramani P., Proximal pointwise contraction, Topology Appl., 2009, 156(18), 2942–2948 http://dx.doi.org/10.1016/j.topol.2009.01.017[Crossref]
  • [3] Boyd D.W., Wong J.S.W., On nonlinear contractions, Proc. Amer. Math. Soc., 1969, 20, 458–464 http://dx.doi.org/10.1090/S0002-9939-1969-0239559-9[Crossref]
  • [4] Derafshpour M., Rezapour Sh., Shahzad N., Best proximity point of cyclic φ-contractions in ordered metric spaces, Topol. Methods Nonlinear Anal., 2011, 37(1), 193–202
  • [5] Di Bari C., Suzuki T., Vetro C., Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 2008, 69(11), 3790–3794 http://dx.doi.org/10.1016/j.na.2007.10.014[WoS][Crossref]
  • [6] Eldred A.A., Veeramani P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 2006, 323(2), 1001–1006 http://dx.doi.org/10.1016/j.jmaa.2005.10.081[Crossref]
  • [7] Jachymski J., Equivalent conditions and the Meir-Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303 http://dx.doi.org/10.1006/jmaa.1995.1299[Crossref]
  • [8] Jachymski J.R., Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., 1997, 125(8), 2327–2335 http://dx.doi.org/10.1090/S0002-9939-97-03853-7[Crossref]
  • [9] Karapınar E., Fixed point theory for cyclic weak ϕ-contraction, Appl. Math. Lett., 2011, 24(6), 822–825 http://dx.doi.org/10.1016/j.aml.2010.12.016[WoS][Crossref]
  • [10] Karpagam S., Agrawal S., Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps, Nonlinear Anal., 2011, 74(4), 1040–1046 http://dx.doi.org/10.1016/j.na.2010.07.026[Crossref]
  • [11] Kirk W.A., Srinavasan P.S., Veeramani P., Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 2003, 4(1), 79–89
  • [12] Kosuru G.S.R., Veeramani P., Cyclic contractions and best proximity pair theorems, preprint available at http://arxiv.org/abs/1012.1434
  • [13] Matkowski J., Integrable Solutions of Functional Equations, Dissertationes Math. (Rozprawy Mat.), 127, Polish Academy of Sciences, Warsaw, 1975
  • [14] Meir A., Keeler E., A theorem on contraction mappings, J. Math. Anal. Appl., 1969, 28, 326–329 http://dx.doi.org/10.1016/0022-247X(69)90031-6[Crossref]
  • [15] Păcurar M., Rus I.A., Fixed point theory for cyclic φ-contractions, Nonlinear Anal., 2010, 72(3–4), 1181–1187 http://dx.doi.org/10.1016/j.na.2009.08.002[Crossref]
  • [16] Petruşel G., Cyclic representations and periodic points, Studia Univ. Babeş-Bolyai Math., 2005, 50(3), 107–112
  • [17] Rus I.A., Cyclic representations and fixed points, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 2005, 3, 171–178
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0145-0
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