Duman, Oktay; Erkuş-Duman, Esra Statistical Korovkin-type theory for matrix-valued functions. (English) Zbl 1265.41053 Stud. Sci. Math. Hung. 48, No. 4, 489-508 (2011). The authors prove that the statistical Korovkin theory, improved by A. D. Gadjiev and C. Orhan [Rocky Mt. J. Math. 32, No. 1, 129–138 (2002; Zbl 1039.41018)] is also valid for the matrix-valued functions. First, they prove a Korovkin-type theorem for the \(A\)-statistical approximation of the mentioned functions (Theorem 2.1). Next, they compute the rate of \(A\)-statistical convergence using the modulus of continuity (Theorem 3.1, Theorem 3.2 and Theorem 4.1). Reviewer: Dan Barbosu (Baia Mare) Cited in 1 Document MSC: 41A36 Approximation by positive operators 41A25 Rate of convergence, degree of approximation 40G15 Summability methods using statistical convergence 65F35 Numerical computation of matrix norms, conditioning, scaling Keywords:\(A\)-statistical convergence; matrix-valued functions; linear positive operators; Korovkin theorem; modulus of continuity; \(A\)-statistical rates of approximation Citations:Zbl 1039.41018 PDFBibTeX XMLCite \textit{O. Duman} and \textit{E. Erkuş-Duman}, Stud. Sci. Math. Hung. 48, No. 4, 489--508 (2011; Zbl 1265.41053) Full Text: DOI