A Note on the (lambda,upsilon)(h)(alpha)-Convergence of the Functions Defined on the Product of Time Scales

Abstract

In this paper, we have introduced the concepts (lambda,upsilon)(h)(alpha)-density of a subset of the product of time scales T-2 and (lambda,upsilon)(h)(alpha)-statistical convergence of order alpha (0 < alpha <= 1) of Delta-measurable function f defined on the product time scale with the help of modulus function h and lambda = (lambda(n)); upsilon = (upsilon(n)) sequences. Later, we have discussed the connection between classical convergence, lambda-statistical convergence and (lambda,upsilon)(h)(alpha)-statistical convergence. In addition, we have seen that f is strongly (lambda,upsilon)(h)(beta) -summable on T then f is (lambda,upsilon)(h)(alpha)-statistical convergent of order alpha.