Open Access

On multivalued nonlinear variational inclusion problems with https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F59836/MediaObjects/13660_2006_Article_1618_IEq1_HTML.gif -accretive mappings in Banach spaces

Journal of Inequalities and Applications20062006:59836

DOI: 10.1155/JIA/2006/59836

Received: 20 January 2006

Accepted: 15 May 2006

Published: 6 July 2006

Abstract

Based on the notion of https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F59836/MediaObjects/13660_2006_Article_1618_IEq2_HTML.gif -accretive mappings and the resolvent operators associated with https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F59836/MediaObjects/13660_2006_Article_1618_IEq3_HTML.gif -accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F59836/MediaObjects/13660_2006_Article_1618_IEq4_HTML.gif -accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F59836/MediaObjects/13660_2006_Article_1618_IEq5_HTML.gif -accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F59836/MediaObjects/13660_2006_Article_1618_IEq6_HTML.gif -uniformly smooth Banach spaces.

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Authors’ Affiliations

(1)
Department of Mathematics, Sichuan University of Science & Engineering

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Copyright

© Heng-You Lan 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.