کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840048 1470505 2014 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Reflexivity is equivalent to the perturbed fixed point property for cascading nonexpansive maps in Banach lattices
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Reflexivity is equivalent to the perturbed fixed point property for cascading nonexpansive maps in Banach lattices
چکیده انگلیسی

Using a theorem of Domínguez Benavides and the Strong James’ Distortion Theorems, we prove that if a Banach space is a Banach lattice, or has an unconditional basis, or is a symmetrically normed ideal of operators on an infinite-dimensional Hilbert space, then it is reflexive if and only if it has an equivalent norm that has the fixed point property for cascading nonexpansive mappings. This new class of mappings strictly includes nonexpansive mappings.Also, using a theorem of Mil’man and Mil’man, we show that for the above classes of Banach spaces, reflexivity is equivalent to the fixed point property for affine cascading nonexpansive mappings.Further, we show that a cascading nonexpansive mapping on a closed, bounded, convex set in a Banach space always has an approximate fixed point sequence.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 95, January 2014, Pages 414–420
نویسندگان
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