King type modification of some positive linear operators

Abstract

In this report, we review some definitions related to approximation theory, which are important for convergence point of view. Then, we study some properties and convergence behaviour for certain linear positive operators. In chapter 1, we recall some linear positive operators I. e. Bernstein polynomials, Szasz-Mirakjan operators, Baskakov operators, Phillips operators, genuine Durrmeyer-type operators etc. We review the main results concerning certain King type modifications of well known sequences of these operators. In chapter 2, we introduce the King type modification of generalized Lupas operators. We obtain auxiliary results for these operators. Then, we study asymptotic formula and error estimation for these operators in terms of second order modulus of continuity. In chapter 3, we show the convergence of King type modification of Lupas operators and comparison with generalised Lupas operators through Graphics in Matlab. Finally, we observe that our modified operators is better than existing Lupas operators.