y1<y2<⋯<yn, and zi=f(yi), i∈[n], where f is a strictly convex function. An example with n=5 is illustrated in the picture (where zi=yi2 and yi=−y6−i). Hereinafter, we think of x, y, z as “vertical,”“left-to-right,” and “to-depth” coordinates in R3, ...
Strongly unique best approximation in uniformly convex banach spaces. Journal of Approximation Theory, 56:101-107.Lin, P.K.: Strongly unique best approximation in uniformly convex Banach spaces. J. Approx. Theor. 56 , 101–107 (1989)P. K. Lin, Strongly unique best approximation in uniformly ...
The existence of a continuous best approximation or of near best approximations of a strictly convex space by a subset is shown to imply uniqueness of the ... PCKK Vogt - 《Journal of Approximation Theory》 被引量: 37发表: 2000年 Discrete Approximations and Fixed Set Iterations in Banach Spa...
There is a hypothesis due to Williamson Hoke [35] that every completely unimodal function (possessing a unique local maximum on every Boolean subcube) can be optimized by the random single switch algorithm in polynomially many steps. The LSP problem exhibits a structure similar to CU-functions (...
Then the function f has a unique fixed point. Proof. Let us define the mapping ϕ as ϕ(x) = F (x, f k(x)) for x ∈ X . The reasoning as in the proof of Theorem 1 leads us to the statement that f k has the unique fixed point y. The point y is of course the ...