This article deals with almost convergence of double sequences using a new generalization of fractional-order difference operator in modular spaces and application to the Korovkin-type approximation in the context of modular spaces for positive linear operators. We then obtain several inclusion relations and present some examples, include proper non-trivial extensions of the corresponding classical ones. Further, we extend our study to new modular forms of Korovkin-type approximation theorems. Finally, we give an example using bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operators and outline possible further extensions and improvements, in order to illustrate the effectiveness of the proposed methods.
"Generalized almost convergence of double sequences in modular function spaces." Adv. Oper. Theory 4 (3) 556 - 573, Summer 2019. https://doi.org/10.15352/aot.1808-1412