Boundedness of Szasz Operators in Half Space Wono Setya Budhi, Oki Neswan, Denny Ivanal Hakim, Ifronika
Institut Teknologi Bandung
Abstract
Let B_n f represents the n-th Bernstein polynomial for f, for each n∈-N and f∈-C[0,1]. Then for any f∈-C[0,1], the sequence {B_n f} converges uniformly to f. However, for functions with continuities, the convergence may fails. A generalization of B_n, denoted by K_n, proposed by Kantorovich as an alternative. Moreover, for every f∈-L^p [0,1],1≤-p≤-∞-, {K_n f} converges to f. It is recommended to approximate integrable functions on half space [0,∞-) using the Szasz operator. In this paper, we show boundedness of the Szasz operators in L^p [0,∞-),1≤-p≤-∞-.
Keywords: Szasz operators, Bounded operators,
Topic: Minisymposia Fourier Analysis and Integral Operators
