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2013 | 11 | 1 | 85-93
Tytuł artykułu

Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

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Języki publikacji
EN
Abstrakty
EN
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
1
Strony
85-93
Opis fizyczny
Daty
wydano
2013-01-01
online
2012-10-24
Twórcy
autor
Bibliografia
  • [1] Banaś J., Chlebowicz A., On existence of integrable solutions of a functional integral equation under Carathéodory conditions, Nonlinear Anal., 2009, 70(9), 3172–3179 http://dx.doi.org/10.1016/j.na.2008.04.020
  • [2] Ben Amar A., Nonlinear Leray-Schauder alternatives for decomposable operators in Dunford-Pettis spaces and application to nonlinear eigenvalue problems, Numer. Funct. Anal. Optim., 2010, 31(11), 1213–1220 http://dx.doi.org/10.1080/01630563.2010.519131
  • [3] Ben Amar A., Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population, Cent. Eur. J. Math., 2011, 9(4), 851–865 http://dx.doi.org/10.2478/s11533-011-0039-6
  • [4] Ben Amar A., The Leray-Schauder condition for 1-set weakly contractive and (ws)-compact operators (manuscript)
  • [5] Ben Amar A., Garcia-Falset J., Fixed point theorems for 1-set weakly contractive and pseudocontractive operators on an unbounded domain, Portugal. Math., 2011, 68(2), 125–147 http://dx.doi.org/10.4171/PM/1884
  • [6] De Blasi F.S., On a property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. R.S. Roumanie, 1977, 21(69) (3–4), 259–262
  • [7] Djebali S., Sahnoun Z., Nonlinear alternatives of Schauder and Krasnosel’skij types with applications to Hammerstein integral equations in L 1 spaces, J. Differential Equations, 2010, 249(9), 2061–2075 http://dx.doi.org/10.1016/j.jde.2010.07.013
  • [8] Emmanuele G., An existence theorem for Hammerstein integral equations, Portugal. Math., 1994, 51(4), 607–611
  • [9] Garcia-Falset J., Existence of fixed points and measures of weak noncompactness, Nonlinear Anal., 2009, 71(7–8), 2625–2633 http://dx.doi.org/10.1016/j.na.2009.01.096
  • [10] Garcia-Falset J., Existence of fixed points for the sum of two operators, Math. Nachr., 2010, 283(12), 1736–1757 http://dx.doi.org/10.1002/mana.200710197
  • [11] Isac G., Gowda M.S., Operators of class (S)1 +, Altman’s condition and the complementarity problem, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 1993, 40(1), 1–16
  • [12] Isac G., Németh S.Z., Scalar derivatives and scalar asymptotic derivatives. An Altman type fixed point theorem on convex cones and some aplications, J. Math. Anal. Appl., 2004, 290(2), 452–468 http://dx.doi.org/10.1016/j.jmaa.2003.10.030
  • [13] Isac G., Németh S.Z., Fixed points and positive eigenvalues for nonlinear operators, J. Math. Anal. Appl., 2006, 314(2), 500–512 http://dx.doi.org/10.1016/j.jmaa.2005.04.006
  • [14] James I.M., Topological and Uniform Spaces, Undergrad. Texts Math., Springer, New York, 1987 http://dx.doi.org/10.1007/978-1-4612-4716-6
  • [15] Kim I.-S., Fixed points, eigenvalues and surjectivity, J. Korean Math. Soc., 2008, 45(1), 151–161 http://dx.doi.org/10.4134/JKMS.2008.45.1.151
  • [16] Latrach K., Taoudi M.A., Existence results for a generalized nonlinear Hammerstein equation on L 1 spaces, Nonlinear Anal., 2007, 66(10), 2325–2333 http://dx.doi.org/10.1016/j.na.2006.03.022
  • [17] Latrach K., Taoudi M.A., Zeghal A., Some fixed point theorems of the Schauder and the Krasnosel’skii type and application to nonlinear transport equations, J. Differential Equations, 2006, 221(1), 256–271 http://dx.doi.org/10.1016/j.jde.2005.04.010
  • [18] Nussbaum R.D., The fixed point index for local condensing maps, Ann. Mat. Pura Appl., 1971, 89, 217–258 http://dx.doi.org/10.1007/BF02414948
  • [19] Schaefer H.H., Topological Vector Spaces, Macmillan, New York, Collier-Macmillan, London, 1966
  • [20] Väth M., Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal., 1999, 13(2), 341–363
  • [21] Zeidler E., Nonlinear Functional Analysis and its Applications. I, Springer, New York, 1986 http://dx.doi.org/10.1007/978-1-4612-4838-5
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0079-6
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