A characterization of the generalized projection with the generalized duality mapping and its applications
Commun. Korean Math. Soc. 2012 Vol. 27, No. 2, 279-296
https://doi.org/10.4134/CKMS.2012.27.2.279
Published online June 1, 2012
Sang Hyeon Han and Sung Ho Park
Sogang University, Sogang University
Abstract : 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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