APPROXIMATION BY TWO DIMENSIONAL GADJIEV-IBRAGIMOV TYPE OPERATORS

Year 2019, Volume: 1 Issue: 1, 1 - 10, 18.01.2019

Nazmiye Gönül Bilgin Numan Özgür

Abstract

In the present paper we introduce linear positive
operators which are defined in [1] by generalization of Gadjiev-Ibragimov
operators and give some approximation properties of these operators in the
space of continuous functions of two variables on a compact set. We find
certain moments of this operator and estimate for approximation error of the
operators in terms of modulus of continuity. Then, we give some approximation
properties of these operators.

Keywords

Gadjiev-Ibragimov Operators, Linear Positive Operators

References

• Ibragimov I. I., and Gadjiev A. D. (1970) On a certain Family of linear positive operators, Soviet Math. Dokl., English Trans., 11, 1092–1095.
• Coskun T. (2012) On the order of weighted approximation by positive linear operators, Turkish J. Math., 36 (1), pp. 113-120.
• Aral A. (2003) Approximation by Ibragimov-Gadjiev operators in polynomial weighted space, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 19 35–44.
• Ghorbanalizadeh, A. M. (2014) On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev-Ibragimov operators, J. Appl. Anal., 20, No. 1, 87–92.
• Gonul N., Coskun E. (2013) Approximation with modified Gadjiev–Ibragimov operators in C[0,A], J. Comput. Anal. Appl., 15 (5) pp. 868-879.
• Gonul N., Coskun E. (2012) Weighted approximation by positive linear operators, Proceedings of IMM of NAS of Azerbaijan, , vol. XXXVI (XLIV), pp. 41-50.