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- W3188752008 abstract "Abstract The purpose of this work is two-fold. On the one side, we focus on the space of real convergent sequences c where we study non-weakly compact sets with the fixed point property. Our approach brings a positive answer to a recent question raised by Gallagher et al. in (J Math Anal Appl 431(1):471–481, 2015). On the other side, we introduce a new metric structure closely related to the notion of relative uniform normal structure, for which we show that it implies the fixed point property under adequate conditions. This will provide some stability fixed point results in the context of hyperconvex metric spaces. As a particular case, we will prove that the set $$M=[-1,1]^mathbb {N}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo>[</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> </mml:mrow> </mml:math> has the fixed point property for d -nonexpansive mappings where $$d(cdot ,cdot )$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>(</mml:mo> <mml:mo>·</mml:mo> <mml:mo>,</mml:mo> <mml:mo>·</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is a metric verifying certain restrictions. Applications to some Nakano-type norms are also given." @default.
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- W3188752008 date "2021-07-22" @default.
- W3188752008 modified "2023-10-13" @default.
- W3188752008 title "New examples of subsets of c with the FPP and stability of the FPP in hyperconvex spaces" @default.
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- W3188752008 doi "https://doi.org/10.1007/s11784-021-00881-1" @default.
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