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On the stability of fixed points and coincidence points of mappings in the generalized Kantorovich’s theorem. (English) Zbl 1473.54046

One of the very important fixed point theorems for self-mappings on a Banach space is Kantorovich’s fixed point theorem (see [L. V. Kantorovich and G. P. Akilov, Functional analysis. Transl. from the Russian by Howard L. Silcock. 2nd ed. Oxford etc.: Pergamon Press (1982; Zbl 0484.46003), Chapter XVIII, Section 1.2, Theorem 1]). This result was extended to the case of metric spaces in [A. V. Arutyunov et al., Proc. Steklov Inst. Math. 304, 60–73 (2019; Zbl 1439.54025); translation from Tr. Mat. Inst. Steklova 304, 68–82 (2019)].
In this very interesting paper, some stability results for single valued and multi valued fixed point problems of Kantorovich type are given.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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