Generalized almost convergence of double sequences in modular function spaces

Document Type: Original Article

Author

‎Gazi University‎, ‎Turkey

Abstract

‎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.

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