Title: On spline quasi-interpolation in cubic spline space <italic>S</italic><sub>3</sub><sup>1,2</sup>(Δ<sub><italic>mn</italic></sub><sup>(2)</sup>)
Abstract: In this paper, by means of the basis composed of two sets of splines with distinct local supports, cubic spline quasi-interpolating operators are investigated on nonuniform type-2 triangulation. These variation diminishing operators based on five mesh points or the center of the support of each spline <italic>B</italic><sub><italic>ij</italic></sub><sup>1</sup> and five mesh points of the support of each spline <italic>B</italic><sub><italic>ij</italic></sub><sup>2</sup> can preserve good approximation, and even reproduce any polynomial of nearly best degrees. Moreover, the spline series can approximate a real sufficiently smooth function uniformly based on the modulus of continuity. And then the convergence results are worked out.