Table 1 The framework of the ILA
From: Some results on an infinite family of accretive operators in a reflexive Banach space
ILA: | Ishikawa-like algorithm (for equilibrium problem ( 3.7 )) |
|---|---|
Step 0: | Choose \(x_{1}\in C\), \(\alpha_{1},\beta_{1},\gamma_{1},\alpha _{1}',\beta_{1}',\gamma_{1}'\in[0,1]\). Set n: = 1. |
Step 1: | Given \(x_{n}\in C\). Choose \(\alpha_{n},\beta_{n},\gamma_{n},\alpha _{n}',\beta_{n}',\gamma_{n}'\in[0,1]\) and compute \(x_{n+1}\in C\) as    \(\begin{array}[t]{l@{\quad}l} F(z_{n},z)+\frac{1}{r}\langle z-z_{n},z_{n}-x_{n}\rangle\geq0,&\forall z\in C,\\ y_{n}=\alpha_{n}'x_{n}+\beta_{n}'z_{n}+\gamma_{n}'e_{n},&\\ x_{n+1}=\alpha_{n} f(x_{n})+\beta_{n}x_{n}+\gamma_{n}y_{n}. & \end{array}\) |
Update n: = n + 1 and go to Step 1. | |