**Approximation and best approximation in function spaces and abstract spaces.**

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 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). - C. Mustăţa, On the approximation of the global extremum of a semi-Lipschitz function, Mediterr. J. Math. 6 (2009), pp. 169-180.

**Theorems of extension and relationship with problems of best approximation.**

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

- 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. - C. Mustăţa, On the Extensions Preserving the Shape of Semi-Holder Function, Results Math. 63 (2013) 425-433.

**Existence and properties of selections associated to the 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.**

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, 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. (pdf)

**Theorems of Korovkin type.**

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