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2012 | 10 | 6 | 2012-2018
Tytuł artykułu

A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

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Języki publikacji
EN
Abstrakty
EN
The existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.
Twórcy
  • Institute of Mathematics, Łódź University of Technology, ul. Wólczańska 215, Łódź, 93-005, Poland, bogdan.przeradzki@p.lodz.pl
Bibliografia
  • [1] Agarwal R.P., O’Regan D., Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: the projective limit approach, J. Appl. Math. Stoch. Anal., 2006, #92375
  • [2] Banas J., Goebel K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York, 1980
  • [3] Burton T.A., Integral equations, implicit functions and fixed points, Proc. Amer. Math. Soc., 1996, 124(8), 2383–2390 http://dx.doi.org/10.1090/S0002-9939-96-03533-2[Crossref]
  • [4] Burton T.A., A fixed-point theorem of Krasnoselskii, Appl. Math. Lett., 1998, 11(1), 85–88 http://dx.doi.org/10.1016/S0893-9659(97)00138-9[Crossref]
  • [5] Garcia-Falset J., Latrach K., Moreno-Gálvez E., Taoudi M.-A., Schaefer-Krasnoselskii fixed point theorems using a usual measure of weak noncompactness, J. Differential Equations, 2012, 252(5), 3436–3452 http://dx.doi.org/10.1016/j.jde.2011.11.012[WoS][Crossref]
  • [6] Granas A., Dugundji J., Fixed Point Theory, Springer Monogr. Math., Springer, New York, 2003
  • [7] 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]
  • [8] Krasnosel’skiĭ M.A., Some problems of nonlinear analysis, In: Amer. Math. Soc. Transl. Ser. 2, 10, American Mathematical Society, Providence, 1958, 345–409
  • [9] Krasnosel’skiĭ M.A., Vaĭnikko G.M., Zabreĭko P.P., Rutitskii Ya.B., Stetsenko V.Ya., Approximate Solution of Operator Equations, Wolters-Noordhoff, Groningen, 1972 http://dx.doi.org/10.1007/978-94-010-2715-1[Crossref]
  • [10] Kryszewski W., Mederski J., Fixed point index for Krasnosel’skii-type set-valued maps on complete ANRs, Topol. Methods Nonlinear Anal., 2008, 28(2), 335–384
  • [11] Liu Y., Li Z., Krasnoselskii type fixed point theorem and applications, Proc. Amer. Math. Soc., 2008, 136(4), 1213–1220 http://dx.doi.org/10.1090/S0002-9939-07-09190-3[Crossref]
  • [12] Ngoc L.T.P., Long N.T., Applying a fixed point theorem of Krasnosel’skii type to the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation, Nonlinear Anal., 2011, 74(11), 3769–3774 http://dx.doi.org/10.1016/j.na.2011.03.021[Crossref][WoS]
  • [13] O’Regan D., Fixed-point theory for the sum of two operators, Appl. Math. Lett., 1996, 9(1), 1–8 http://dx.doi.org/10.1016/0893-9659(95)00093-3[Crossref]
  • [14] Sadovskiĭ B.N., Limit-compact and condensing operators, Uspehi Mat. Nauk, 1972, 27(1), 81–146 (in Russian)
  • [15] Xiang T., Krasnosel’skii fixed point theorem for dissipative operators, Electron. J. Differential Equations, 2011, #147
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.doi-10_2478_s11533-012-0102-y
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