Deferred Cesàro Summability and Korovkin-Type Approximation Theorems for Double Sequences on Time Scales

This paper investigates fundamental concepts of statistical convergence for double sequences of time-scale functions via the deferred Cesàro summability mean. Several limit properties and inclusion relations between the newly-introduced convergence notions are established. Based on these concepts, a number of Korovkin-type approximation theorems are proved for time-scale functions of two variables by using suitable algebraic test functions. Illustrative examples involving a positive linear operator associated with bivariate Bernstein polynomials are presented to demonstrate the applicability of the theoretical results. In addition, the rate of statistical convergence with respect to the deferred Cesàro summability method is studied and estimated.