A new technique for convergence theorem of fixed point problem of quasi-nonexpansive mapping
Kanyarat Cheawchan, Suthep Suantai, Atid Kangtunyakarn · Fixed Point Theory and Applications · 2015
Abstract 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 $W_{\omega}:= (1-\omega )I+\omega W$ W ω : = ( 1 − ω ) I + ω W , where W is a quasi-nonexpansive mapping and $\omega\in (0,\frac{1}{2} )$ ω ∈ ( 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.