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Table 1 Iterates of modified Mann, modified Picard-Mann hybrid, and modified Picard-Ishikawa hybrid iterations for \(\pmb{x_{1}=1.5}\)

From: A new iterative scheme for numerical reckoning fixed points of total asymptotically nonexpansive mappings

Iterate

The modified Mann iteration process

The modified Picard-Mann hybrid iteration

The modified Picard-Ishikawa hybrid iteration

\(x_{1}\)

1.50000000000000

1.50000000000000

1.50000000000000

\(x_{2}\)

1.13188130791299

0.95198821855406

1.00000000000000

\(x_{3}\)

1.04396043597100

1.00000000000000

1.00000000000000

\(x_{4}\)

1.01099010899275

1.00000000000000

1.00000000000000

\(x_{5}\)

1.00219802179855

1.00000000000000

1.00000000000000

\(x_{6}\)

1.00036633696643

1.00000000000000

1.00000000000000

\(x_{7}\)

1.00005233385235

1.00000000000000

1.00000000000000

\(x_{8}\)

1.00000654173154

1.00000000000000

1.00000000000000

\(x_{9}\)

1.00000072685906

1.00000000000000

1.00000000000000

\(x_{10}\)

1.00000007268591

1.00000000000000

1.00000000000000

\(x_{11}\)

1.00000000660781

1.00000000000000

1.00000000000000

\(x_{12}\)

1.00000000055065

1.00000000000000

1.00000000000000

\(x_{13}\)

1.00000000004236

1.00000000000000

1.00000000000000

\(x_{14}\)

1.00000000000303

1.00000000000000

1.00000000000000

\(x_{15}\)

1.00000000000020

1.00000000000000

1.00000000000000