Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces

Kong, Dezhou; Liu, Lishan; Wu, Yong Hong

doi:10.1007/s11784-016-0337-5

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Authors

Kong, Dezhou

Liu, Lishan

Wu, Yong Hong

Date

2016

Type

Journal Article

Metadata

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Citation

Kong, D. and Liu, L. and Wu, Y.H. 2016. Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces. Journal of Fixed Point Theory and Applications: pp. 1-15.

Source Title

Journal of Fixed Point Theory and Applications

DOI

10.1007/s11784-016-0337-5

ISSN

1661-7738

School

Department of Mathematics and Statistics

URI

http://hdl.handle.net/20.500.11937/52192

Collection

Curtin Research Publications

Abstract

© 2016 Springer International PublishingIn this paper, we discuss isotonicity characterizations of the metric projection operator, including its necessary and sufficient conditions for isotonicity onto sublattices in Banach spaces. Then, we demonstrate their applications to variational inequalities and fixed point theory in Banach spaces. Our work generalizes many existing results obtained in earlier work.