Abstract: "Each continuous function is approximable by algebraic polynomials". The most constructive proof of the above theorem concerning the approximation of continuous functions on a compact interval by polynomials, we use some sequence of positive linear operators. It can be mentioned that the more usual tools of Analysis like the Taylors's polynomials and Lagrange's interpolation are not appropriate to the problem of Uniform Approximation of continuous functions. The degree of approximation of positive linear operators by certain classes of functions is considered as the classical problem. The main purpose of the talk is to discuss the problem for the degree of approximation of certain classes of functions using Summability sums as the positive linear operators.

Brief Biography of the Speaker:
Prof. Syed Huzoorul Hasnain Khan is a Professor of Mathematics, Department of Mathematics AMU Aligarh India since 1998. Prof. Khan has thirty six years of teaching and research experience and successfully guided students for Ph.D. He has published twenty six research papers in various Journals of International repute and is the author of eight books for undergraduate as well as postgraduate programs which are recommended as text books in many Indian Universities. He is the reviewer for Mathematical Reviews and Zentrablatt fur Mathematik und ihre Grenzgebrete. Life member of many Mathematical Societies in India and abroad, President Asian Mathematical Ecological Society ( ICTP, ITALY 1996-1999) and the Chairman Department of Mathematics AMU Aligarh India (2006-2009).