Document Type: Original Article
Gazi University, Turkey
This paper deals with almost convergence of double sequences using a new generalization of fractional-order difference operator in modular spaces and application to 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-Szsaz-Kantorovich-Charlier-type operators and outline possible further extensions and improvements, in order to illustrate the effectiveness of the proposed methods.