The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes which elements mimic as well as possible the Chebyshev-Loba...

In this paper we introduce an algorithm for computing nonlinear continuous Chebyshev approximations. The algorithm is based on successive linearizations within adaptively adjusted neighborhoods. The convergence of the algorithm is proven under some general assumptions such that it is applicable for many Chebyshev approximation problems discussed in the literature. It, like the Remez exchange me...

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors of a finitedimensional semimodule over an idempotent semifield, and subject to boundary constraints. The solution approach is implemented, whi...

A unified approach is presented for determining all the constants Ym.n (m > 0, n > 0) which occur in the study of real vs. complex rational Chebyshev approximation on an interval. In particular, it is shown that Ym,m+2 = 1/3 (m > 0), a problem which had remained open.