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Zbl 1151.47057
Wu, Ke-Qing; Huang, Nan-Jing
Properties of the generalized $f$-projection operator and its applications in Banach spaces.
(English)
[J] Comput. Math. Appl. 54, No. 3, 399-406 (2007). ISSN 0898-1221

The concept of a generalized $f$-projection operator was introduced by the authors in [Bull.\ Aust.\ Math.\ Soc.\ 73, No.\,2, 307--317 (2006; Zbl 1104.47053)]. In the present paper, they show that the generalized $f$-projection operator is a generalization of the resolvent operator for the subdifferential $\partial f$ of a proper, convex and lower semi-continuous functional $f$ from Hilbert spaces to Banach spaces. From this result, it is deduced that the generalized $f$-projection operator is maximal monotone. In the final section of the paper, the authors investigate an iterative method of approximating solutions for a class of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces.
[Srinivasa Swaminathan (Halifax)]
MSC 2000:
*47J20 Inequalities involving nonlinear operators
47J25 Methods for solving nonlinear operator equations (general)

Keywords: generalized $f$-projection operator; generalized variational inequality; maximal monotone operator; lower semi-continuity; iterative sequence; convergence

Citations: Zbl 1104.47053

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