A new technique for convergence theorem of fixed point problem of quasi-nonexpansive mapping

作者：Cheawchan Kanyarat; Suantai Suthep; Kangtunyakarn Atid^*

来源：Fixed Point Theory and Applications, 2015, 2015(1): 216.

DOI：10.1186/s13663-015-0453-8

• quasi-nonexpansive mapping
• equilibrium problem
• variational inequality problem
• fixed point problem

For the purpose of this paper, we use the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the set of solutions of a modified system of variational inequalities without demiclosed condition of W and W-omega := (1 - omega)/ + omega W, where W is a quasi-nonexpansive mapping and omega epsilon (0, 1/2) in the framework of Hilbert space. By using our main result, we obtain a strong convergence theorem involving a finite family of nonspreading mappings and another corollary. Moreover, we give a numerical example to encourage our main theorem.

• 出版日期2015-11-25