Deferred weighted 𝒜-statistical convergence based upon the (<italic>p</italic>,<italic>q</italic>)-Lagrange polynomials and its applications to approximation theorems.

Recently, the notion of positive linear operators by means of basic (or <italic>q</italic>-) Lagrange polynomials and 𝒜 {\mathcal{A}} -statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of <italic>q</italic>-Lagrange polynomials and <italic>A</italic>-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911–6918]. In our present investigation, we introduce a certain deferred weighted 𝒜 {\mathcal{A}} -statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, <italic>t</italic> and t 2 {t^{2}} defined on a Banach space C ⁢ [ 0 , 1 ] {C[0,1]} for a sequence of (presumably new) positive linear operators based upon ( p , q ) {(p,q)} -Lagrange polynomials. Furthermore, we investigate the deferred weighted 𝒜 {\mathcal{A}} -statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper. [ABSTRACT FROM AUTHOR]