Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2013 | 11 | 1 | 85-93
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
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.
Opis fizyczny
  • Université de Gafsa, Cité Universitaire
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [10] Garcia-Falset J., Existence of fixed points for the sum of two operators, Math. Nachr., 2010, 283(12), 1736–1757
  • [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
  • [13] Isac G., Németh S.Z., Fixed points and positive eigenvalues for nonlinear operators, J. Math. Anal. Appl., 2006, 314(2), 500–512
  • [14] James I.M., Topological and Uniform Spaces, Undergrad. Texts Math., Springer, New York, 1987
  • [15] Kim I.-S., Fixed points, eigenvalues and surjectivity, J. Korean Math. Soc., 2008, 45(1), 151–161
  • [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
  • [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
  • [18] Nussbaum R.D., The fixed point index for local condensing maps, Ann. Mat. Pura Appl., 1971, 89, 217–258
  • [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
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.