[1] Freud G.  Uber einseitige approximation durch polynome I. Acta Sci Math Szeged, 1955, 16: 12--18

[2] Korneichuk Ⅱ H, et al. Approximation with restrictions (in Russian).  ⅡYMKA, KucB, 1982

[3] Popov  V A. Onesided approximation of periodic functions of serveral variables. Comp Rend Acad Bulg Sci,  1982, 35(12): 1639--1642

[4]  Hristov V H, Ivanov K G. Operators for Onesided Approximation of Functions. Sofia: Constructive Theory of Functions'87, 1988

[5] Liu Y P. Average σ-K width of class of L_p(R^d) in L_q(R^d). Chin Ann Math, 1995, 16B(3): 351--360

[6] Jiang  Y J,   Liu Y P.  Average width and optimal recovery of multivarivariate Besov-Wiener classes. J Math Study, 1988, 331(4): 353--361

[7]  Xu G Q,  Liu Y P. The average widths of Sobolev-Wiener classes and Besov-Wiener classes. Acta Mathematica Sinica, English Series, 2004, 20(1): 81--92

[8]  Liu Y P,  Xu G Q. The average widths and non-linear widths of the classes of multivariate functions with bounded moduli of smoothness. Acta Mathematica Sinica, English Series, 2002, 18(4): 663--674

[9] Liu Y P, Xu G Q. Widths and average widths of sobolev classes. Acta Mathematica Scientia, 2003, 23B(2): 178--184

[10] Pustovoitov N N. Representation and approximation of multivariate periodic functions with agiven modulus of smoothness. Analysis Math, 1994, 20: 35--48

[11] Ivanov K G. On the behaviour of two moduli of functions II. Serdica Bulg Math Publ, 1986, 12: 196--203

[12] Popov V A. On the one-sided approximation of multivariate functions//Chui C K, Schumaker L L, Ward J D, eds.
Approximation Theory IV. New York: London, 1983: 657--661

[13] Magaril-Ⅱ' yaev G G. Average widths of Sobolev classes on Rⁿ.  J  Approx Theory, 1994, 76(1): 65--76