Approximation Theory

Approximation and best approximation, extension results, selections

Results regarding the uniqueness and the characterization of the elements of best approximation were obtained for the problem of best approximation in a metric space and in the spaces with asymmetric norms:

Results regarding the extension for Lipschitz and Holder functions, preserving the smallest constants or supplementary properties such as convexity, boundedness, etc.:

Linear and positive operators

Umbral calculus

Results related to the construction and the properties of some approximation operators in the expressions of which appear binomial sequences, Appell sequences and Sheffer sequences: