Szâsz-Kantorovich operators type based on bivariate brenke type polynomials

This thesis contains 5 chapters. The first chapter is devoted to the introduction In the second chapter, some basic definitions and theorems in analysis and approximation theory are given. In the third chapter, the rate of convergence of Szâsz-Kantorovich operators based on Brenke type polynomials is studied with the help of the modulus of continuity , Voronovskaja type theorem and Peetre's-K functional. In the fourth chapter, the bivariate generalization of Szâsz-Kantorovich operators based on Brenke type polynomials is defined and the degree of approximation of these operators is given in terms of the total and partial modulus of continuity, Lipschitz class and Peetre's-K functional. Further the approach of these operators in weighted spaces has been studied. Finally, the associated generalized Boolean sum operators of Szâsz-Kantorovich operators based on Brenke type polynomials is defined and the degree of approximation in the Bögel continuous functions space is estimated by means of the mixed modulus of smoothness and Lipschitz class. The fifth chapter is devoted to the conclusion.