On a fixed-point theorem
Copyright policy )On a fixed-point theorem
This note has discussed three fixed point theorems for mappings \(T:H\times H\to H\), where \(H\) is a suitable subset of a metric or normed linear space, satisfying certain conditions. Only indications of the proofs are given. The first two theorems are proved with the help of a theorem due to \textit{M. Edelstein} [J. Lond. Math. Soc. 37, 74-79 (1962; Zbl 0113.16503)]. For the last theorem, a theorem of \textit{F. E. Browder} [Proc. Natl. Acad. Sci. USA 54, 1041-1044 (1965; Zbl 0128.35801)] concerning a nonexpanding mapping is used.
Fixed-point theorems, measure of noncompactness, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., nonexpanding mapping, fixed point theorems
Fixed-point theorems, measure of noncompactness, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., nonexpanding mapping, fixed point theorems
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