Abstract and Applied Analysis

Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces

Hiroko Manaka

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Let E be a smooth Banach space with a norm · . Let V ( x , y ) = x 2 + y 2 - 2  x , J y 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.

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Abstr. Appl. Anal., Volume 2015, Special Issue (2015), Article ID 760671, 9 pages.

First available in Project Euclid: 17 August 2015

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Manaka, Hiroko. Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces. Abstr. Appl. Anal. 2015, Special Issue (2015), Article ID 760671, 9 pages. doi:10.1155/2015/760671. https://projecteuclid.org/euclid.aaa/1439816297

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