APPROXIMATION PROPERTIES OF GENERALIZED BLENDING TYPE LOTOTSKY-BERNSTEIN OPERATORS

Abstract

In this paper, we introduce a family of blending type Bernstein operators L-n(alpha,s) (f;x) which depends on two parameters, alpha and s. We prove a Korovkin type approximation theorem and obtain the rate of convergence of these operators. We also prove that these operators has monotonicity and convexity preserving properties for each alpha and s. So far, Lotosky matrices that generates blending type Bernstein operators were ignored. In this paper, we also introduce Lototsky matrices that generates these new family of blending type Bernstein operators.