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J. Korean Math. Soc. 2017; 54(2): 493-506

Online first article December 7, 2016      Printed March 1, 2017

https://doi.org/10.4134/JKMS.j160068

Copyright © The Korean Mathematical Society.

U-flatness and non-expansive mappings in Banach spaces

Ji Gao and Satit Saejung

Community College of Philadelphia, Khon Kaen University

Abstract

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In this paper, we define the modulus of $n$-dimensional $U$-flatness as the determinant of an $(n+1)\times(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.

Keywords: fixed point property, matrices, modulus of $n$-dimensional uniform flatness, modulus of $n$-dimensional $U$-flatness, non-expansive mapping, normal structure

MSC numbers: 46B20, 47H10, 37C25, 54H25

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