Some classes of uniformly convergent interpolation processes on the roots of Chebyshev polynomials

Abstract. In this paper we construct discrete processes on the roots of four kinds of Chebyshev polynomials supplemented with some endpoints of \([-1,1]\) by using suitable summations generated by a function \(\varphi\). Our aim is to investigate these methods regarding the interpolation property and uniform convergence in the Banach space \(\left(C[-1,1],\|\cdot\|_\infty\right)\). With proper conditions on \(\varphi\) we obtain wide classes of interpolation processes which are uniformly convergent for every function \(f\in C[-1,1]\).