Approximate Solutions of Common Fixed-Point Problems by Alexander J. Zaslavski

Author:Alexander J. Zaslavski
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(6.155)

(6.156)

(6.157)

Set

(6.158)

Let k ≥ 0 be an integer. By ( 6.2), ( 6.153), ( 6.155), and ( 6.156), for each and each ,

(6.159)

(6.160)

(6.161)

and

(6.162)

In view of ( 6.144), ( 6.150), and ( 6.160)–( 6.162), for each integer k ≥ 0, each and each ,

(6.163)

Assume that

(6.164)

In view of ( 6.158) and ( 6.164),

(6.165)

By ( 6.153), there exists such that

(6.166)

By ( 6.165) and ( 6.166),

(6.167)

It follows from ( 6.156), ( 6.157), and ( 6.167) that there exists for which

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