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The purpose of this paper is to investigate the effects of fourdimensional summability matrix methods on the A-statistical approximation of sequences of positive linear operators defined on the space of all real valued B¨ogel-type continuous functions on a compact subset of the real line. Furthermore, we study the rates of A-statistical convergence in our approximation.

Mathematics Subject Classification (2010): 41A25, 41A36.

Keywords: The Korovkin theorem, B-continuous functions, rates of Astatistical convergence for double sequences, regularity for double sequences.