STUDY ON SOME GENERALISED APPROXIMATION OPERATORS

Abstract

This thesis is mainly a study of convergence estimates of various approximation opera tors. Approximation theory is indeed an old topic in mathematical analysis that remains an appealing field of study with several applications. The findings presented here are related to the approximation of specific classes of linear positive operators. The introduc tory chapter is a collection of relevant definitions and literature of concepts that are used throughout this thesis. • The second chapter is based on Durrmeyer-type modification of Apostol-Genocchi operators. • The third chapter is devoted to a modification of the Lupa¸s-Kantrovich operator that preserves exponential function e −x . • The fourth chapter is based on the inverse Pólya-Eggenberger distribution. • The chapter fifth is dedicated to estimating the difference between Mastroianni and Gupta operators. • The chapter sixth is dedicated to Micchelli-type iterative combinations of general ized positive linear operators. • The last chapter summarizes the thesis with a brief conclusion and also discusses the prospects of this thesis.