Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces

Hiroko Manaka

Abstract and Applied Analysis, 2015, vol. 2015, 1-9

Abstract:

Let be a smooth Banach space with a norm . Let for any , where stands for the duality pair and is the normalized duality mapping. We define a -strongly nonexpansive mapping by . This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a -strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:760671

DOI: 10.1155/2015/760671

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