Minimum-norm solution of variational inequality and fixed point problem in banach spaces

Abstract

We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an-inverse strongly monotone mapping and a fixed point of relatively non-expansive mapping in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of non-linear operators.

Keywords:

• Monotone mappings
• relatively asymptotically non-expansive mappings
• relatively non-expansive
• strong convergence
• variational inequality problems

AMS Subject Classifications:

• 47H05
• 47H09
• 47H10
• 47J05
• 47J25.

Acknowledgments

The authors would like to thank the referee for valuable suggestions which helped to improve this manuscript.