Direct and inverse theorems for the Bézier variant of certain summation-integral type operators

Authors : Asha Ram GAIROLA, P. N. AGRAWAL

Pages : 221-234

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Recently, the Bézier variant of some well known operators were introduced insert ignore into journalissuearticles values(cf. [8]-[9]); and their rates of convergence for bounded variation functions have been investigated insert ignore into journalissuearticles values(cf. [2], [10]);. In this paper we establish direct and inverse theorems for the Bézier variant of the operators Mn introduced in [5] in terms of Ditzian-Totik modulus of smoothness wj\lambdainsert ignore into journalissuearticles values(f,t); insert ignore into journalissuearticles values(0 \leqslant l \leqslant1 );. These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.
Keywords : Degree of approximation, Ditzian Totik modulus of continuity