In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

Several techniques are known to compute a new orthogonal polynomial φk+1 of degree k + 1 from Lk := span{φ0, ..., φk} in case of (discrete) orthogonality on the real line. In the Arnoldi approach one chooses Φk ∈ Lk and makes xΦk orthogonal against φ0, ..., φk. By taking as Φk a linear combination of φk and the kernel (or GMRES) polynomial ψk(x) = ∑k j=0 φj(0)φj(x), one needs to orthogonalize o...

An orthogonality space is a set X together with symmetric and irreflexive binary relation ⊥, called the relation. A block partition of maximal mutually orthogonal elements X, decomposition collection subsets each which complement union others. (X,⊥) normal if any gives rise to unique space. The one-dimensional subspaces Hilbert equipped usual provides motivating example. Together maps that are,...

In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends functions to obtain analytic solutions in a uniform form rapidly convergent series the posed Sobolev space. Using Gram-Schmidt orthogonality process, complete orthogonal essential are obtained compact...

The purpose of this paper is to introduce and discuss the concept of orthogonality in the fuzzy metric spaces. At last we introduce and discuss the concept of orthogonality in the fuzzy normed spaces, and obtain some results on orthogonality in fuzzy normed spaces similar to orthogonality in normed spaces.