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Some properties of measures of noncompactness in paranormed spaces


Author: Olga Hadžić
Journal: Proc. Amer. Math. Soc. 102 (1988), 843-849
MSC: Primary 47H10; Secondary 47H09
DOI: https://doi.org/10.1090/S0002-9939-1988-0934854-1
MathSciNet review: 934854
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Abstract: This paper presents new properties of important measures of noncompactness in paranormed spaces. Using these properties some fixed point theorems for multivalued mappings in general topological vector spaces are obtained in a straightforward way.


References [Enhancements On Off] (What's this?)

  • [1] J. Daneš, Some fixed point theorems, Comment. Math. Univ. Carolin. 9 (1968), 223-235. MR 0235435 (38:3744)
  • [2] K. Fan, Fixed-point and minimal theorems in locally convex topological vector spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121-126. MR 0047317 (13:858d)
  • [3] O. Hadžić, Some fixed point and almost fixed point theorems of multivalued mappings in topological vector spaces, Nonlinear Anal. 5 (1980), 1009-1019. MR 633015 (82k:47073)
  • [4] -, On equilibrium point in topological vector spaces, Comment. Math. Univ. Carolin. 23 (1982), 727-738. MR 687567 (84c:47057)
  • [5] -, Fixed point theorems for multivalued mappings in not necessarily locally convex topological vector spaces, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 14 (1984), 27-40. MR 850239 (87h:47121)
  • [6] -, Fixed point theory in topological vector spaces, Univ. of Novi Sad, Faculty of Science, Institute of Mathematics, 1984, 337 pp. MR 789224 (87m:47127)
  • [7] S. Hahn, A fixed point theorem in general topological vector spaces, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 15 (1985). MR 849757 (87j:47086)
  • [8] -, Fixpunktsätze für limeskompatke mengenwertige Abbildungen in nicht notwending lokalkonvexen topologischen Vektorräumen, Comment. Math. Univ. Carolin. (to appear).
  • [9] C. J. Himmelberg, J. R. Porter, and F. S. Van Vleck, Fixed point theorems for condensing multifunctions, J. Math. Anal. Appl. 38 (1972), 205-207.
  • [10] T. Jerofsky, Zur Fixpunkttheorie mengenwertiger Abbildungen, Diss. A, Tech. Univ. Dresden, 1983.
  • [11] V. Klee, Leray-Schauder theory without local convexity, Math. Ann. 141 (1960), 286-296. MR 0131150 (24:A1004)
  • [12] C. Krauthausen, Der Fixpunktsatz von Schauder in nicht notwendig konvexen Räumen sowie Anwendungen auf Hammerstein'sche Gleichungen, Diss., Aachen, 1976.
  • [13] A. J. Porter, An elementary version of the Leray-Schauder theorem, J. London Math. Soc. (2) 5 (1972), 414-416. MR 0312342 (47:904)
  • [14] T. Reidrich, Die Räume $ {L^p}(0,1)(0 < p < 1)$ sind zulässig, Wiss. Z. Tech. Univ. Dresden 12 (1963), 1149-1152.
  • [15] -, Der Raum $ S(0,1)$ ist zulässig, Wiss. Z. Tech. Univ. Dresden 13 (1964), 1-6.
  • [16] R. Schöneberg, Leray-Schauder principles for condensing multivalued mappings in topological linear spaces, Proc. Amer. Math. Soc. 72 (1978), 268-270. MR 507320 (81b:47075)
  • [17] C. H. Su and V. M. Sehgal, Some fixed point theorems for condensing multifunctions in locally convex spaces, Proc. Amer. Math. Soc. 50 (1975), 150-154. MR 0380530 (52:1430)
  • [18] E. Tarafdar and R. Vyborny, Fixed point theorems for condensing multivalued mappings in a locally convex topological space, Bull. Austral. Math. Soc. 12 (1975), 161-170. MR 0383167 (52:4048)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934854-1
Keywords: Fixed points, measure of noncompactness, paranormed spaces
Article copyright: © Copyright 1988 American Mathematical Society

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