Weighted αβ-equistatistical Convergence for Double Sequences of Functions of Two Variables
AbstractKarakaya and T.A. Chiristi extended the definition of statistical convergence to weighted statistical convergence in , using the sequence of real numbers , satisfying some conditions. The modification of this topic was fulfilled in some papers such as  and . It is well known that if , for all k, the weighted statistical convergence reduces to statistical convergence. Karakaya and Karasia  defined weighted -statistical convergence of order , which does not have this property. In this extension for the case , for all k, weighted -statistical convergence of order does not reduce to -statistical convergence. Later Aktuğlu and Halil introduced a modification in  to remove this extension problem. In this paper we introduce weighted -equistatistical convergence of order for double sequences, by using two real sequences and , considering the modified extension with improved method, also we use this definition to prove Korovkin type approximation theorem via weighted -equistatistical convergence of order and weighted -statistical uniform convergence of order for bivariate functions on . Some examples of positive linear operators are constructed to show that, our approximation results work, but its uniform case does not work. Furthermore rate of weighted -equistatistical convergence of order are studied.
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