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On some fixed point problems of non-expansive mapping and shrinking mapping. (English) Zbl 1314.47068
Summary: D. R. Smart in his book [Fixed point theorems. London: Cambridge University Press (1974; Zbl 0297.47042)]’ raised some problems to describing the fixed point properties of non-expansive mapping and shrinking mapping. In this paper, we have introduced and solved these fixed point problems connecting to non-expansive mapping and shrinking mapping. Here we have also introduced and solved two other fixed point problems of non-expansive mapping where the mapping is defined on the Hilbert space.
##### MSC:
 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems
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