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Table 2 Iterates of modified Mann, modified Picard-Mann hybrid, and modified Picard-Ishikawa hybrid iterations for \(\pmb{x_{1}=1.9}\)

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

\(x_{1}\)

1.90000000000000

1.90000000000000

1.90000000000000

\(x_{2}\)

1.13027756377320

0.95262315543817

1.00000000000000

\(x_{3}\)

1.04342585459107

1.00000000000000

1.00000000000000

\(x_{4}\)

1.01085646364777

1.00000000000000

1.00000000000000

\(x_{5}\)

1.00217129272955

1.00000000000000

1.00000000000000

\(x_{6}\)

1.00036188212159

1.00000000000000

1.00000000000000

\(x_{7}\)

1.00005169744594

1.00000000000000

1.00000000000000

\(x_{8}\)

1.00000646218074

1.00000000000000

1.00000000000000

\(x_{9}\)

1.00000071802008

1.00000000000000

1.00000000000000

\(x_{10}\)

1.00000007180201

1.00000000000000

1.00000000000000

\(x_{11}\)

1.00000000652746

1.00000000000000

1.00000000000000

\(x_{12}\)

1.00000000054395

1.00000000000000

1.00000000000000

\(x_{13}\)

1.00000000004184

1.00000000000000

1.00000000000000

\(x_{14}\)

1.00000000000299

1.00000000000000

1.00000000000000

\(x_{15}\)

1.00000000000020

1.00000000000000

1.00000000000000