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

• Main Authors: Piri Hossein, Badali Ali
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Fixed Point Theory and Applications
• Subjects: projection; common fixed point; amenable semigroup; iterative process; strong convergence; variational inequality
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2011/1/55

<p>Abstract</p> <p>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 <it>&#946;</it>-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.</p> <p> <b>Mathematics Subject Classification 2000: </b>47H09, 47H10, 43A07, 47J25</p>