On the existence and convergence of approximate solutions for mixed variational-like inequalities

Abstract

The auxiliary principle technique is extended to develop an iterative algorithm for finding approximate solutions of a mixed variational-like inequality in a real Hilbert space. Not only the existence of approximate solutions of a mixed variational-like inequality is proven, but also the strong convergence of approximate solutions to an exact solution of a mixed variational-like inequality is shown. The convergence criteria presented in this article are new.

Keywords:

• Auxiliary principle technique
• Convergence
• Existence
• Mixed variational-like inequality

Keywords:

• MS (2000) Subject Classifications: 49J40
• 47H04
• 47H19

Acknowledgements

This research was partially supported by grant from the National Science of Council of Taiwan and by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai.