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Iterative construction of fixed points for multivalued operators of the monotone type in uniformly smooth Banach spaces. (English) Zbl 0823.47056

Summary: The fixed points of set-valued operators satisfying a condition of monotonicity type in \(s\)-uniformly smooth Banach spaces are approximated by a recursive averaging process.

MSC:

47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
47J25 Iterative procedures involving nonlinear operators
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References:

[1] Chidume, C. E., Iterative consturction of fixed points for multivalued operators of the monotone type.Appl. Anal.,23 (1986), 209–218. · Zbl 0597.47039 · doi:10.1080/00036818608839641
[2] Dunn, J. C., Iterative construction of fixed points for multivalued operators of the monotone type.J. Funct. Anal.,27 (1978), 38–50. · Zbl 0422.47033 · doi:10.1016/0022-1236(78)90018-6
[3] Istratescu, Vasile I.,Fixed Point Theory, D. Reidel Publishing Company (1981). · Zbl 0465.47035
[4] Lindenstrauss, J. and L. Tsafriri,Classical Banach Spaces, II., Springer-Verlag, New York Berlin (1979).
[5] Xu, Z. B. and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach Spaces,J. Math. Anal. Appl.,157 (1991), 189–210. · Zbl 0757.46034 · doi:10.1016/0022-247X(91)90144-O
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