AUTHORS: Octavian Agratini

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ABSTRACT: We present two general sequences of positive linear operators. The first is introduced by using a class of dependent random variables, and the second is a mixture between two linear operators of discrete type. Our goal is to study their statistical convergence to the approximated function. This type of convergence can replace classical results provided by Bohman-Korovkin theorem. A particular case is delivered.

KEYWORDS: Positive linear operator, Bohman-Korovkin theorem, statistical convergence, Bernstein operator, Baskakov operator

REFERENCES:

[1] O. Agratini, On some new operators of discrete type, Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 68, 2002, 229-243.

[2] O. Agratini, Linear operators generated by a probability density function, pp. 1-12, In: Advances Constructive Approximation: Vanderbilt 2003, M. Neamt¸u and E.B. Saff (eds.), Nashboro Press, Brentwood, TN, 2004.

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[5] A.D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math., Vol. 32, 2002, 129-138.

[6] T. Sal ˘ at, On statistically convergent sequences ´ of real numbers, Math. Slovaca, Vol. 30, 1980, 139-150.