%0 Journal Article %T Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities %A Piri Hossein %A Badali Ali %J Fixed Point Theory and Applications %D 2011 %I Springer %X In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for ¦Â-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common element of the above two sets. Mathematics Subject Classification 2000: 47H09, 47H10, 43A07, 47J25 %K projection %K common fixed point %K amenable semigroup %K iterative process %K strong convergence %K variational inequality %U http://www.fixedpointtheoryandapplications.com/content/2011/1/55