Abstract Korovkin type theorems on modular spaces by $\mathscr{A}$-summability

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 143 (2018) MATHEMATICA BOHEMICA No. 4, 419-430

$\mathcal{F-}$relative $\mathcal{A-}$summation process for double sequences and abstract Korovkin type theorems

“…That's why Nishishiraho introduced and studied the notion of A−summation process on a compact Hausdorff space ( [27,28]). Afterwards Korovkin-type theorems are studied via A−summation process in various spaces like weighted spaces (see [2,3]), modular spaces ( [10,17,29,31,35,36]). In the present paper, we introduce the notions of F−relative modular convergence and F−relative strong convergence for double sequences of functions and we prove our main Korovkin-type theorems via F−relative A−summation process on modular spaces.…”