Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces

Hiroko Manaka

Abstract and Applied Analysis, 2015, vol. 2015, issue 1

Abstract: Let E be a smooth Banach space with a norm ‖·‖. Let V(x, y) = ‖x‖2 + ‖y‖2 − 2 〈x, Jy〉 for any x, y ∈ E, where 〈·, ·〉 stands for the duality pair and J is the normalized duality mapping. We define a V‐strongly nonexpansive mapping by V(·, ·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a V‐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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https://doi.org/10.1155/2015/760671

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:760671

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