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&#8712-N and f&#8712-C[0,1]. Then for any f&#8712-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&#8712-L^p [0,1],1&#8804-p&#8804-&#8734-, {K_n f} converges to f. It is recommended to approximate integrable functions on half space [0,&#8734-) using the Szasz operator. In this paper, we show boundedness of the Szasz operators in L^p [0,&#8734-),1&#8804-p&#8804-&#8734-.

Keywords: Szasz operators, Bounded operators,

Topic: Minisymposia Fourier Analysis and Integral Operators