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Uniform noncompact convexity, fixed point property in modular spaces. (English) Zbl 0820.47063

Summary: We define the so-called modulus of noncompact convexity in modular spaces. We extend the results obtained in Banach spaces by Goebel and Sekowski although their methods can not be reproduced.

MSC:

47H10 Fixed-point theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46A80 Modular spaces
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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