In this paper we present a new algorithm for the two-dimensional fixed point problem f(x)=x on the domain [0, 1] × [0, 1], where f is a Lipschitz continuous function with respect to the infinity norm, with constant 1. The computed approximation x satisfies ||f(x) − x||. [ e for a specified tolerance e < 0.5. The upper bound on the number of required function evaluations is given by 2Klog 2 (1/e)L+1. Similar bounds were derived for the case of the 2-norm by Z.
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