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The iterative approximation method for fixed points of \(\Phi\)-hemicontractive mapping and applications. (English) Zbl 1158.47054

In this work, the authors introduce the concept of \(\Phi\)-hemicontractive self-mapping \(T\) of a real Banach \(X\) into itself, as a generalization of the usual \(\Phi\)-hemicontractive mapping. The strong convergence of the generalized Mann iterative sequence with random errors to the unique fixed point of the operator is proved, after imposing appropriate conditions on the parameters of the iteration scheme, where the operator \(T\) is \(\Phi\)-hemicontractive on \(X\).

MSC:

47J25 Iterative procedures involving nonlinear operators
47H06 Nonlinear accretive operators, dissipative operators, etc.
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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