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Some results about T-stability and almost T-stability. (English) Zbl 1281.47052
Let \(X\) be a normed space and \(T: X \to X\) an operator with a unique fixed point. In this paper, the authors study: (i) the almost stability of Mann iteration, when \(T\) is a \( \varphi \)-contraction; (ii) the stability of Picard iteration for \( T \) satisfying a contractive condition of integral type.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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