Browder-Krasnoselskii-type fixed point theorems in Banach spaces. (English) Zbl 1218.47078
The authors give some fixed point theorems for the sum \(A+B\) of a weakly-strongly continuous operator and a nonexpansive operator on a Banach space \(X\). An operator \(A:M\rightarrow M\) is called weakly-strongly continuous if for each sequence \(\left\{ x_{n}\right\} \) in \(M\) which converges weakly to \( x\) in \(M\), the sequence \(\left\{ Ax_{n}\right\} \) converges strongly to \(Ax\). Their results improve several results obtained by D. E. Edmunds [Math. Ann. 174, 233–239 (1967; Zbl 0152.34701)], J. Reinermann [Math. Z. 119, 339–344 (1971; Zbl 0204.45802)], S. P. Singh [Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 54 (1973) 558–561 (1974; Zbl 0287.47040)], D. O’Regan [Math. Comput. Modelling 27, No. 5, 1–14 (1998; Zbl 1185.34026)], and others.
Reviewer: M. Serban (Cluj-Napoca)
MSC:
47H10 | Fixed-point theorems |
47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
weakly-strongly continuous operator; nonexpansive operator; Browder-Krasnoselskij-type fixed point theoremsReferences:
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