Statistical Relative $$\mathcal {A}$$ A -Summation Process and Korovkin-Type Approximation Theorem on Modular Spaces

Modüler Uzaylar Üzerinde P-İstatistiksel A-Toplam Süreci Aracılığıyla Yaklaşım

“…As in the proof of Theorem 1 in [18], because of ρ is N -quasi semiconvex and strongly finite, we can see that…”

“…Orhan and Demirci [17] presented A-summation process and then Kolay et al [18] presented relative A-summation process on a modular space as follows:…”

“…Note that the scale function in an A-summation process is a non-zero constant, making it a special case of a relative A-summation process [18].…”

“…It is the reason why Nishishiraho introduced and studied the notion of A-summation process on a compact Hausdorff space [44,45]. Recently, Kolay et al have studied an approximation theorem of statistical type via relative A-summation process in modular function space in [18].…”

$\mathcal{F-}$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.…”