coefficient and free term on the close interval [0 , 1]. The second example shows us the uniformconvergence of the numerical solution in case of integrable coefficient and free term which are only continuous on the interval [0 , 1[. The third example
defined on CL(X � Y). These topologies are inherited by the set G(X, Y) of closed-graph multifunctions from X to Y, if we identify each multifunction with its graph. Finally, we consider the topology of uniform convergence τuc on the set F(X, 2Y) of all closed-valued multifunctions, i.e. functions from X to the set (CL(Y),
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].
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 .
In this note noncommutative versions of Etemadi's SLLN and Petrov's SLLN are given. As a noncommutative counterpart of the classical almost sure convergence, the almost uniform convergence of measurable operators is used.