Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities

Abstract

Abstract 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 β-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

Keywords

• projection
• common fixed point
• amenable semigroup
• iterative process
• strong convergence
• variational inequality