New Generalization of f-Best Simultaneous Approximation in Topological Vector Spaces

Abstract EN

Let K be a nonempty subset of a Hausdorff topological vector space X, and let f be a real-valued continuous function on X.

If for each x=(x1,x2,…,xn)∈Xn, there exists k0∈K such that FK(x)=∑i=1nfxi-k0=inf∑i=1nf(xi-k):k∈K, then K is called f-simultaneously proximal and k0 is called f-best simultaneous approximation for x in K.

In this paper, we study the problem of f-simultaneous approximation for a vector subspace K in X.

Some other results regarding f-simultaneous approximation in quotient space are presented.