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Agarwal, Ravi P.; O’Regan, Donal; Taoudi, Mohamed-Aziz

Browder-Krasnoselskii-type fixed point theorems in Banach spaces. (English) Zbl 1218.47078

Fixed Point Theory Appl. 2010, Article ID 243716, 20 p. (2010).
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)

Cited in 1 Review
Cited in 23 Documents

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 theorems

Citations:

Zbl 0152.34701; Zbl 0204.45802; Zbl 0287.47040; Zbl 1185.34026
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References:

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