Approximation Theory

Linear and positive operators

U. Abel, O. Agratini, M. Ivan, Asymptotic properties of Kantorovich-type Szász–Mirakjan operators of higher order, Mathematical Foundations of Computing, 2023, https://doi.org/10.3934/mfc.2023003
U. Abel, O. Agratini, Simultaneous approximation by Gauss–Weierstrass–Wachnicki operators, Mediterr. J. Math., 19 (2022) no. 6, art. 267, https://doi.org/10.1007/s00009-022-02194-0
O. Agratini, S.G. Gal, On Landau-type approximation operators, Mediterranean Journal of Mathematics, 18 (2021) art. no. 64, https://doi.org/10.1007/s00009-021-01712-w
O. Agratini, A. Aral, Approximation of some classes of functions by Landau type operators, Results in Mathematics, 76 (2021) art. no. 12
O. Agratini, Shift λ – invariant operators, Constructive Mathematical Analysis, 2 (2019) 3, 103-108. doi: 10.33205/cma.544094

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.

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: