Fixed points of several classes of nonlinear mappings in Banach space

Kuhfittig, Peter K. F.

doi:10.1090/S0002-9939-1974-0346607-6

Fixed points of several classes of nonlinear mappings in Banach space
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by Peter K. F. Kuhfittig PDF

Proc. Amer. Math. Soc. 44 (1974), 300-306 Request permission

Abstract:

In the first part of the paper conditions for the existence of ordinary and higher order fixed points of individual and commutative families of nonlinear operators are obtained. The second part deals with the existence of fixed points of an operator $T:C \to X$ whose graph is closed in the Cartesian product topology induced by the strong topology in $C$ and the weak topology in $X$. The convergence to fixed points of sequences of successive approximations is considered in both parts.

References

Felix E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044. MR 187120, DOI 10.1073/pnas.54.4.1041
F. E. Browder and W. V. Petryshyn, The solution by iteration of linear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 566–570. MR 190744, DOI 10.1090/S0002-9904-1966-11543-4
Ralph DeMarr, Common fixed points for commuting contraction mappings, Pacific J. Math. 13 (1963), 1139–1141. MR 159229
M. Edelstein, A remark on a theorem of M. A. Krasnoselski, Amer. Math. Monthly 73 (1966), 509–510. MR 194866, DOI 10.2307/2315474
W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006. MR 189009, DOI 10.2307/2313345