Fixed Points for Mean Non-expansive Mappings

Authors: Wu, Chun-xue1; Zhang, Li-juan2

Source: Acta Mathematicae Applicatae Sinica, Volume 23, Number 3, July 2007 , pp. 489-494(6)

Publisher: Springer

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Abstract:

For a Banach Space X Garcia-Falset introduced the coefficient R(X) and showed that if R(X) < 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that ∥Tx − Ty∥ ≤ ax − y∥ + bx − Ty∥ for any x, yX, where a, b ≥ 0, a + b ≤ 1. We show that if then T has a fixed point in X.

Keywords: Fixed point property; O175; mean non-expansive mapping; normal structure

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s10255-007-0388-x

Affiliations: 1: Email: wuchunxue1020@163.com 2: Email: lijuanzhang99@163.com

Publication date: July 1, 2007

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