Weak fixed point property for nonexpansive mappings with respect to orbits in Banach spaces |
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| Authors: | A Amini-Harandi M Fakhar H R Hajisharifi |
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| Institution: | 1.Department of Mathematics,University of Isfahan,Isfahan,Iran;2.School of Mathematics,Institute for Research in Fundamental Sciences (IPM),Tehran,Iran;3.Department of Mathematics,Khansar Faculty of Mathematics and Computer Sciences,Khansar,Iran |
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| Abstract: | In this paper, we first show that a Banach space X has weak normal structure if and only if X has the weak fixed point property for nonexpansive mappings with respect to (wrt) orbits. Then, we give a counterexample to show that the Goebel–Karlovitz lemma does not hold for minimal invariant sets of nonexpansive mappings wrt orbits, and we present a modified version of the Goebel–Karlovitz lemma. |
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