A Review on Summability Theory with Degree of Approximation

Abstract

The study of sum ability has always been of great interest, as it occupies a very prominent position in analysis. Modern mathematicians have made the subject very interesting. The convergence problems associated make the subject part of analysis rather than algebra, However, the theory of sum ability and approximation has applications to several branches of mathematics such as the theory of functions, signal analysis, etc. The study of sequence space was motivated by the classical results of sum ability theory which were obtained by several notable mathematicians such as Cesaro, Holder, Abel, Norlund, Euler, Knopp, Hardy, and others. Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby the approximation of functions by generalized Fourier series, that is, approximations based upon the summation of a series of terms based upon orthogonal polynomials.