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Commun. Korean Math. Soc. 2012; 27(2): 279-296
Printed June 1, 2012
https://doi.org/10.4134/CKMS.2012.27.2.279
Copyright © The Korean Mathematical Society.
A characterization of the generalized projection with the generalized duality mapping and its applications
Sang Hyeon Han and Sung Ho Park
Sogang University, Sogang University
In this paper, we define a generalized duality mapping, which is a generalization of the normalized duality mapping and using this, we extend the notion of a generalized projection and study their properties. Also we construct an approximating fixed point sequence using the generalized projection with the generalized duality mapping and prove its strong convergence.
Keywords: Banach spaces, normalized and generalized duality mappings, generalized projection, approximating fixed point sequence
MSC numbers: 47H10, 46B20
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