Geometrical coefficients and the structure of the fixed-point set of asymptotically regular mappings in Banach spaces |
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Authors: | Jaros?aw Górnicki |
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Institution: | Department of Mathematics, Rzeszów University of Technology, P.O. Box 85, 35-959 Rzeszów, Poland |
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Abstract: | It is shown that if E is a separable and uniformly convex Banach space with Opial’s property and C is a nonempty bounded closed convex subset of E, then for some asymptotically regular self-mappings of C the set of fixed points is not only connected but even a retract of C. Our results qualitatively complement, in the case of a uniformly convex Banach space, a corresponding result presented in T. Domínguez, M.A. Japón, G. López, Metric fixed point results concerning measures of noncompactness mappings, in: W.A. Kirk, B. Sims (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publishers, Dordrecht, 2001, pp. 239-268]. |
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Keywords: | primary 47H09 47H10 secondary 47B20 54C15 |
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