Viscosity approximation to a common solution of variational inequality problems and fixed point problems for Lipschitzian semigroup in Banach spaces
Poom Kumam, Somyot Plubtieng, Phayap Katchang · Mathematical sciences · 2013
Abstract We introduce a new iterative algorithm based on a viscosity approximation method for finding the common solution of variational inequality problems for an inverse strongly accretive operator and the solution of fixed point problems for Lipschitzian semigroup mappings in Banach spaces. In controlling suitable conditions, strong convergence theorems are proven. Our results extend and improve the recent results of some authors in the literature in this field. MSC 2000 47H10; Secondary 47H09, 43A07, 47H20, 47J20