Generalized Szász–Mirakyan operators in the variation seminorm

Source abstract

The aim of the present paper is to introduce generalized Szász–Mirakyan operators. This article studies the property of variation seminorm and some approximation properties of generalized Szász–Mirakyan operators not only in normed spaces but also in variation seminorm. We obtain convergence properties of our operators using of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s K functional. We also give asymptotic formula and the convergence of the derivatives for these operators. We investigate the variation detracting property of generalized Szász–Mirakyan operators. We show the convergence of generalized Szász–Mirakyan operators in variation seminorm and its rate of convergence invariation seminorm.