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:

• C. Mustăţa, On the extremal semi-Lipschitz functions, Rev. Anal. Numer. Theor. Approx. 31 (2002) Nr. 1, 103-108.
• C. Mustăţa, S. Cobzaş, Extension of bilinear functionals and best approximation in 2-normed space, Studia Univ. “Babes-Bolyai”, Seria Mathematica, XLIII (1998) no. 2, 1-13.
• C. Mustăţa, S. Cobzaş, Extension of bounded linear functionals and best approximation in space with asymmetric norm, Rev. Anal. Numer. Theor. Approx., 33 (2004) no. 1, 39-50.

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

• C. Mustăţa, Şt. Cobzaş, Norm preserving extension of convex Lipschitz functions, J. Approx. Theory 24 (1978) no. 3, 238-244
• C. Mustăţa, Best approximation and unique extension of Lipschitz functions, J. Approx. Theory 19 (1977) no. 3, 222-230
• C. Mustăţa, Extension of semi Lipschitz function on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx., 30 (2001) nr. 1, 61-67.

Linear and positive operators

• O. Agratini, A. Aral, Approximation of some classes of functions by Landau type operators, Results in Mathematics, 76 (2021) art. no. 12

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:

• M. Crăciun, Procedee de aproximare construite cu ajutorul calculului umbral, Editura Risoprint, Cluj-Napoca, 2008.
• M. Crăciun, Approximation operators constructed by means of Sheffer sequences, Rev. Anal. Numer. Theor. Approx., 30 (2001) no. 2, 135-150.