On a property of moduli of smoothness and K-functionals


A new property of moduli of smoothness associated to functions belonging to some certain spaces is revealed. In terms of statistical convergence, we determine the behavior of these special functions at the point |(\delta=0\). In this respect, Peetre’s \(K\)-functional is also investigated.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Moduli of smoothness, K-functional, statistical convergence

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O. Agratini, On a property of moduli of smoothness and K-functionals, Filomat, 29 (2015) no. 7, pp. 1425-1428. https://doi.org/10.2298/FIL1507425A


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[1] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its Applications, de Gruyter Studies in Mathematics, Vol. 17, Walter de Gruyter, Berlin, 1994.

[2] Z. Ditzian, V. Totik, Moduli of Smoothness, Springer Series in Computational Mathematics, Vol. 9, Springer Verlag, New York Inc., 1987.

[3] O. Duman, M.K. Khan, C. Orhan, A-Statistical convergence of approximating operators, Math. Inequal. Appl., 6(2003), 689-699.

[4] H. Fast, Sur le convergence statistique, Colloq. Math. 2 (1951) 241-244.

[5] A.D. Gadjiev, C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002) 129-138.

[6] M. Mursaleen, O.H.H. Edely, On invariant mean and statistical convergence, Appl. Math. Lett. 22 (2009) 1700-1704.

[7] T. Nishishiraho, The degree of convergence of positive linear operators. Tˆohoku Math. Journal 29 (1977) 81-89.

[8] J. Peetre, A Theory of Interpolation of Normed Spaces, Notas de Matem´atica, Instituto de Matem´atica Pura e Aplicada, Rio de Janeiro 39 (1968) 1-86.

[9] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980) 139-150.

[10] H. Steinhauss, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.


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