EXISTENCE AND APPROXIMATION OF SOLUTION OF THE VARIATIONAL INEQUALITY PROBLEM WITH A SKEW MONOTONE OPERATOR DEFINED ON THE DUAL SPACES OF BANACH SPACES

Authors

  • S. Plubtieng DEPARTMENT OF MATHEMATICS , FACULTY OF SCIENCE , NARESUAN UNIVERSITY, PHITSANULOK 65000, THAILAND
  • W. Sriprad DEPARTMENT OF MATHEMATICS , FACULTY OF SCIENCE , NARESUAN UNIVERSITY, PHITSANULOK 65000, THAILAND

Abstract

In this paper, we first study an existence theorem of the variational inequality problem for a skew monotone operator defined on the dual space of a smooth Banach space. Secondary, we prove a weak convergence theorem for finding a solution of the variational inequality problem by using projection algorithm method with a new projection which was introduced by Ibaraki and Takahashi [T. Ibaraki, W. Takahashi, A new projection and convergence theorems for the projections in Banach spaces, Journal of Approximation Theory 149 (2007),1-14]. Further, we apply our convergence theorem to the convex minimization problem and the problem of finding a zero point of the maximal skew monotone operator

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Published

2011-12-18

How to Cite

Plubtieng, S., & Sriprad, W. (2011). EXISTENCE AND APPROXIMATION OF SOLUTION OF THE VARIATIONAL INEQUALITY PROBLEM WITH A SKEW MONOTONE OPERATOR DEFINED ON THE DUAL SPACES OF BANACH SPACES. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 1(1), 23-33. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/42

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Section

Research Article