The aim of this paper is to continue the investigation of the second author started in , where a weighted version of a
classical result of P. Erdős was proved using Freud type weights. We shall show that an analogous statement is true for weighted
interpolation if we consider exponential weights on [-1,1].
We give a weighted Hermite–Fejr type interpolation process on the half line. On suitable Laguerre nodes it converges for
continuous functions which fulfil a certain not too fast growing property at zero and infinity.
The aim of this paper is to continue our investigations started in , where we studied the summability of weighted Lagrange
interpolation on the roots of orthogonal polynomials with respect to a weight function w. Starting from the Lagrange interpolation polynomials we constructed a wide class of discrete processes which are uniformly
convergent in a suitable Banach space (Cρ, ‖‖ρ) of continuous functions (ρ denotes (another) weight). In  we formulated several conditions with respect to w, ρ, (Cρ, ‖‖ρ) and to summation methods for which the uniform convergence holds. The goal of this part is to study the special case when
w and ρ are Freud-type weights. We shall show that the conditions of results of  hold in this case. The order of convergence
will also be considered.
Starting from the Lagrange interpolation on the roots of Jacobi polynomials, a wide class of discrete linear processes is
constructed using summations. Some special cases are also considered, such as the Fejr, de la Valle Poussin, Cesro, Riesz
and Rogosinski summations. The aim of this note is to show that the sequences of this type of polynomials are uniformly convergent
on the whole interval [-1,1] in suitable weighted spaces of continuous functions. Order of convergence will also be investigated.
Some statements of this paper can be obtained as corollaries of our general results proved in .
We give a weighted Hermite-Fejr-type interpolatory method on the real line, which is a positive operator on “good” matrices.
We give an example on “good” interpolatory matrix by weighted Fekete points. To prove the convergence theorem we need the
generalization of “Rodrigues’ property”.