Table 1 Iterates of modified Mann and modified Picard-Mann hybrid iterations
From: Modified Picard-Mann hybrid iteration process for total asymptotically nonexpansive mappings
Iterate | \(\boldsymbol {x_{1}=1.1}\) | \(\boldsymbol {x_{1}=1.5}\) | \(\boldsymbol {x_{1}=1.9}\) | |||
|---|---|---|---|---|---|---|
Iteration ( 1.1 ) | Iteration ( 1.3 ) | Iteration ( 1.1 ) | Iteration ( 1.3 ) | Iteration ( 1.1 ) | Iteration ( 1.3 ) | |
\(x_{2}\) | 1.03218253804965 | 0.98903980508798 | 1.13188130791299 | 0.95198821855406 | 1.13027756377320 | 0.95262315543817 |
\(x_{3}\) | 1.01072751268322 | 1.00000000000000 | 1.04396043597100 | 1.00000000000000 | 1.04342585459107 | 1.00000000000000 |
\(x_{4}\) | 1.00268187817080 | 1.00000000000000 | 1.01099010899275 | 1.00000000000000 | 1.01085646364777 | 1.00000000000000 |
\(x_{5}\) | 1.00053637563416 | 1.00000000000000 | 1.00219802179855 | 1.00000000000000 | 1.00217129272955 | 1.00000000000000 |
\(x_{6}\) | 1.00008939593903 | 1.00000000000000 | 1.00036633696643 | 1.00000000000000 | 1.00036188212159 | 1.00000000000000 |
\(x_{7}\) | 1.00001277084843 | 1.00000000000000 | 1.00005233385235 | 1.00000000000000 | 1.00005169744594 | 1.00000000000000 |
\(x_{8}\) | 1.00000159635605 | 1.00000000000000 | 1.00000654173154 | 1.00000000000000 | 1.00000646218074 | 1.00000000000000 |
\(x_{9}\) | 1.00000017737289 | 1.00000000000000 | 1.00000072685906 | 1.00000000000000 | 1.00000071802008 | 1.00000000000000 |
\(x_{10}\) | 1.00000001773729 | 1.00000000000000 | 1.00000007268591 | 1.00000000000000 | 1.00000007180201 | 1.00000000000000 |
\(x_{11}\) | 1.00000000161248 | 1.00000000000000 | 1.00000000660781 | 1.00000000000000 | 1.00000000652746 | 1.00000000000000 |
\(x_{12}\) | 1.00000000013437 | 1.00000000000000 | 1.00000000055065 | 1.00000000000000 | 1.00000000054395 | 1.00000000000000 |
\(x_{13}\) | 1.00000000001034 | 1.00000000000000 | 1.00000000004236 | 1.00000000000000 | 1.00000000004184 | 1.00000000000000 |
\(x_{14}\) | 1.00000000000074 | 1.00000000000000 | 1.00000000000303 | 1.00000000000000 | 1.00000000000299 | 1.00000000000000 |
\(x_{15}\) | 1.00000000000005 | 1.00000000000000 | 1.00000000000020 | 1.00000000000000 | 1.00000000000020 | 1.00000000000000 |
\(x_{16}\) | 1.00000000000000 | 1.00000000000000 | 1.00000000000001 | 1.00000000000000 | 1.00000000000001 | 1.00000000000000 |
\(x_{17}\) | 1.00000000000000 | 1.00000000000000 | 1.00000000000000 | 1.00000000000000 | 1.00000000000000 | 1.00000000000000 |