With the theory of interpolation by Thiele type vector valued continued fractions, a series of interpolation functions are produced.

In this paper, a new method for constructing a segment of circular arc is presented by using the vector valued continued fractions, and the center and radius of this arc are given.

In the literature related,the GC′ continuity parametric rational circular arc spline has been constructed in the plane by means of vector valued continued fractions interpolants,and the tangent vector of the first knot can be adjusted to preserve the shape of the spline,but the general principle of adjusting the tangent vector has not been given,which is inconvenient for practical use.

In this paper, a new method is presented for constructing a segment of circular arc in two or three dimension space by use of the vector valued continued fraction, and the center and radius of the circular arc are also given.

New convergence criterion for vector valued continued fractions;

In the literature related,the GC1 continuity parametric rational circular arc spline has been constructed in the plane by means of vector valued continued fractions interpolants,but the general algorithm about the parametric rational circular arc spline in the three-dimensional space has not been given.

In this paper,we first establish an equivalence between a vector variational inequality problem and a generalized variational inequality problem.

A class of generalized multi-valued vector variational inequality problem(in short GMVVIP) is studied in Hausdorff topological vector space.

By using the vector variational inequality related to radial epiderivative,we give a number of necessary and sufficient conditions for Henig efficiency,super efficiency and cone-super efficiency of set-valued optimization under the framework of locally convex topological vector spaces,which generalizes some known related results.