Journal Press India^®

Author Details ( * ) denotes Corresponding author

This paper introduced a generalization of mixed summation integral type operators with Szász and Baskakov Basis, so-called Szász Baskakov operator. Then the moment estimates of these operators have been obtained and the uniform convergence has been established. Further, the quantitative approximation and local approximation behavior of the operators has been studied using modulus of continuity and Lipschitz class function. Then, it has been proved that the rate of convergence of the proposed operators is better than their primitives. In the last section, r−th order generalization of modified operators has been introduced and their rate of convergence has been estimated.

Keywords

Szász Baskakov Operator; Positive Linear Operator; Korovokin Type Approximation Theorem; Modulus of Smoothness; Lipschitz Class; Peetre’s Type k–Functional; Voronovskaya Type Theorem.

1. O Agratini, Linear operators that preserve some test function, Int. J. Math. Math. Sci. Art I.D. 94136, 2006,11


2. RA DeVore, GG Lorentz. Constructive Approximation, Springer, Berlin,1993.


3. O Duman, MA Ozarslan, H Aktuglu. Better error estimation for Szász-Mirakjan-Beta operators, J. Comput. Anal. 4, 2008, 53-59.


4. O Duman, MA Ozarslan. Szász-Mirakjan type operators providing a better error estimation, Appl. Math. Lett. 20, 2007, 1184-1188.


5. F Altomare, M Campiti. Korovkin-type Approximation Theory and its Application, Walter de Gruyter Studies in Math., , de Gruyter and Co., Berlin, 17, 1994.