LARGE CLASSES WITH THE FIXED POINT PROPERTY IN A DEGENERATE LORENTZ-MARCINKIEWICZ SPACE

LARGE CLASSES WITH THE FIXED POINT PROPERTY IN A DEGENERATE LORENTZ-MARCINKIEWICZ SPACE

V. Nezir, H. Dutta, M. Yazıcı

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Abstract

Recently, Nezir has renormed `1 and observed that the resulting space turns out be a degenerate Lorentz-Marcinkiewicz space. Then, xed point properties have been investigated for the space, its dual and its predual. Also, inspiring from the study of Goebel and Kuczumow, as they showed for the Banach space of absolutely summable sequences `1, Nezir showed that a class of non-weak* compact, closed, convex and bounded sets in one of these spaces has the xed point property for ane nonexpansive mappings. In fact, very recently, generalizing the equivalent norm on `1, Nezir and Mustafa obtained new type of degenerate Lorentz-Marcinkiewicz spaces with their xed point properties and got the analogy of Goebel and Kuczumow's for the resulting space. In this paper, we show that there exists large classes of non-weak* compact, closed, convex and bounded sets with the xed point property for ane nonexpansive mappings in the generalized degenerate Lorentz-Marcinkiewicz space.

Keywords

nonexpansive mapping, nonre exive Banach space, xed point property, closed bounded convex set, Lorentz-Marcinkiewicz spaces.