Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means...

A Korovkin type theorem is established in the space C̃b[0,∞) of all uniformly continuous and bounded functions on [0,∞) for a sequence of positive linear operators, the approximation error being estimated with the aid of the usual modulus of continuity. As applications we obtain quantitative results for q-Baskakov operators. Mathematics Subject Classification (2010): 41A36, 41A25.

Abstract Employing some properties of multivariate Baskakov–Durrmeyer operators and utilizing modified K -functional a decomposition technique, the authors obtain direct theorem weak type inverse in Orlicz spaces.

Abstract In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad many well-known operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta, Lupa?-Beta, Lupa?-Szász, genuine Bernstein-Durrmeyer, and P?lt?nea. We first find direct estimates in terms second-order modulus continuity, then an estimate error Ditzian-Totik smoothne...

Khan [4] and Mishra [5] have proved some results dealing with the degree of approximation of functions in Lpspaces using different types of operators. BaskakovDurrmeyer operators were first considered by Sahai-Prasad [8] in 1985 . Sinha et al. [9] improved and corrected the results of [8]. In 2005, Finta [1], introduced a new type of Baskakov-Durrmeyer operator by taking the weight function of ...

In the present paper, we introduce some Stancu type generalization of Szász-Mirakyan-Baskakov type operators. We estimate the moments for these operators using the hypergeometric series, which can be related to Laguerre polynomials. We estimate point wise convergence, asymptotic expansion and error estimate in terms of higher order modulus of continuity of function in simultaneous approximation...

We characterize the functions defined on a weighted space, which are uniformly approximated by a sequence of positive linear operators and we obtain the range of the weights which can be used for uniform approximation. We, also, obtain an estimation of the remainder in terms of the usual modulus of continuity. We give particular results for the Szász-Mirakjan and Baskakov operators. Mathematics...