Study Of Approximation Properties For Certain Sequences Of Positive Linear Operators And Applications

Abstract

Abstract of the thesis entitled Study of Approximation Properties for Certain Sequences newlineof Positive Linear Operators and Applications to be submitted by Ms. newlineMamta Rani (Reg. No: 170806001), Department of Mathematics, Faculty of Science newlinefor the award of Doctor of Philosophy in Mathematics. newlineThis thesis is divided into six chapters. Chapter 1 is an introductory part of the thesis newlinewhich deals with the background of approximation theory, some notations and basic newlinedefinitions which are used throughout the thesis. newlineChapter 2 includes the Literature Survey. In 1885Weierstrass gave the approximation newlinetheorem . The proof of this theorem was very difficult to understand. Many mathematicians newlineintroduced various proofs of this celebrated theorem. were given by many newlinefamous researchers like Jackson(1911), de la Vallee Poussin(1908), Landau(1908), newlineFejer (1900), Runge(1885), Lebesgue(1898), Volterra(1897), Lerch(1892 and 1903), newlinePicards (1891). In 1912, Berenstein established the proof of Weierstrass theorem newlinewhich is very useful and well known in theory of approximation. Recently, a generalization newlineof Bernstein Polynomial is presented which is termed as l-Bernstein operators newlinefor l 2 [0,1]. In this chapter, we present a literature for these sequences of operators. newlineBy motivating with this literature, we construct several sequences of operators which newlineare discussed in the next chapters. newline