Approximation Theory

(in Romanian )

Approximation and best approximation in function spaces and abstract spaces.

Some theorems of characterization and unicity of the elements of best approximation were obtained in the problem of best approximation in a metric space and in the spaces with asymmetric norms.

• C. Mustăţa, On the best approximation in metric spaces, Rev. Anal. Numer. Theor. Approx., 31 (2002) no. 1, 103-108 (citations in ISI journals)
• C. Mustăţa, On the extremal semi-Lipschitz function, Mathematica - Rev. Anal. Numer. Theor. Approx 4 (1975) 1, 45-50 (citations).
• 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 (citations).
• 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 (citations).
• S. Cobzaş, C. Mustăţa, Best approximation in spaces with asymmetric norm, Rev. Anal. Numer. Theor. Approx., 35 (2006) no. 1, 17-31 (citations).

Theorems of extension and relationship with problems of best approximation.

Some theorems of extension for Lipschitz and Holder functions, preserving the smallest constants and/or suplementaries properties (convexity, boundedness, etc) are obtained.

• C. Mustăţa, Best approximation and unique extension of Lipschitz functions, J. Approx. Theory, 19 (1977) 3, 222-230
• C. Mustăţa, Extension of Holder functions and some related problems of best approximation, "Babes-Bolyai" Univ., Research Seminars, Seminar on Mathematical Analysis, Preprint no. 7 (1991), 71-86. (citations in ISI journals)
• C. Mustăţa, Extension of semi Lipschitz function on quasi-metric spaces, Rev. Anal. Numer. Theor. Approx., 30 (2001) nr. 1, 61-67 (citations in ISI journals)
• C. Mustăţa, A Phelps type result for spaces with asymmetric norms, Bul. St. Univ. Baia Mare, XVIII, Serie B (2002) no. 2, 275-280.

Existence and study of properties for selections associated to metric projection.

Theorems for selection for metric projection over a cone in a normed space with applicatons in concrete cases are given.

• C. Mustăţa, Selections associated to Mc Shane's extension theorem for Lipschitz functions, Rev. Anal. Numer. Theor. Approx., 21 (1992) 2, 135-145.
• C. Mustăţa, S. Cobzaş, Selections associated to the metric projection, Rev. Anal. Numer. Theor. Approx., 24 (1995) nos. 1-2, 45-52 (citations).

Approximation by linear and positive operators. Umbral calculus.

We obtained results related to the construction and study of 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, iv+180 pp, ISBN 978-973-751-908-5.
• M. Crăciun, Approximation operators constructed by means of Sheffer sequences, Rev. Anal. Numer. Theor. Approx., 30 (2001) no. 2, 135-150.

Theorems of Korovkin type.

Theorems of Korovkin type were given in the paper

• C. Mustăţa, D. Andrica, An abstract Korovkin type theorem and applications, Studia Univ. "Babes-Bolyai", XXXIV (1989) fasc. 2, 44-41 (citations).