Synchronal algorithm and cyclic algorithm for fixed point problems and variational inequality problems in hilbert spaces

Abstract

Abstract We design synchronal algorithm and cyclic algorithm based on the general iterative algorithm proposed by Tian in 2010 for finding the common fixed point x* of finite family of strict pseudo-contractive mappings which is the solution of the variational inequality 〈(γ f - μF)x*, x - x*〉 ≤ 0, . 2000 Mathematics Subject Classification: 58E35; 47H09; 65J15.

Keywords

• strict pseudo-contractions
• nonexpansive mapping
• variational inequality
• synchronal algorithm
• cyclic algorithm
• fixed point