Korovkin type approximation for double sequences via statistical A-summation process on modular spaces
Abstract
theorems on modular spaces via statistical A-summation process for
double sequences of positive linear operators and we construct an example
satisfying our new approximation theorem but does not satisfy
the classical one.
Keywords
Full Text:
PDFReferences
Bardaro, C., Boccuto, A., Dimitriou, X., Modular convergence theorems for abstract sampling operators, Applicable Analysis, 92(2013), no. 11, 2404-2423.
Bardaro, C., Mantellini, I., Approximation properties in abstract modular spaces for a class of general sampling-type operators, Appl. Anal. 85(2006), 383-413.
Bardaro, C., Musielak,J., Vinti,G., Nonlinear integral operators and applications, de Gruyter Series in Nonlinear Analysis and Appl. Vol., 9 Walter de Gruyter Publ., Berlin, 2003.
Bardaro, C., Mantellini, I., Korovkin's theorem in modular spaces, Commentationes Math. 47(2007), 239-253.
Bardaro, C., Mantellini, I., A Korovkin theorem in multivariate modular function spaces, J. Funct. Spaces Appl. 7(2009), no. 2, 105-120.
Boos, J., Classical and Modern Methods in Summability, Oxford University Press, Oxford, 2000.
Çakan, C. and Altay, B., Statistically boundedness and statistical core of double sequences, J. Math. Anal. Appl., 317(2006), 690-697.
Fast, H., Sur la convergence statistique, Colloq, Math., 2 (1951), 241-244.
Karakuş, S. and Demirci, K., A-summation process and Korovkin-type approximation theorem for double sequences of positive linear operators, Mathematica Slovaca, textbf62(2012), 281-292.
Karakuş, S., Demirci, K., Matrix summability and Korovkin type approximation theorem on modular spaces, Acta Math. Univ. Comenianae, 79(2010), no.2, 281-292.
Karakuş, S., Demirci, K., Duman, O., Statistical approximation by positive linear operators on modular spaces, Positivity 14(2010), 321-334.
Korovkin, P. P., Linear operators and approximation theory, Hindustan Publ. Corp., Delhi, 1960.
Kozlowski, W. M., Modular function spaces, Pure Appl. Math. 122 Marcel Dekker, Inc., New York, 1988.
Mantellini, I., Generalized sampling operators in modular spaces, Commentationes Math., 38(1998), 77-92.
Moricz, F., Statistical convergence of multiple sequences, Arch. Math., 81(2004), 82-89.
Musielak, J., Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034 Springer-Verlag, Berlin, 1983.
Musielak, J., Nonlinear approximation in some modular function spaces I, Math. Japon. 38(1993), 83-90.
Orhan, C. and Sakaoglu, _I., Rate of convergence in Lp approximation, Periodica Math.Hungarica, 68(2014), no. 2,176-184.
Orhan S., Demirci, K., Statistical A-Summation Process and Korovkin Type Approximation Theorem on Modular Spaces, Positivity 18(2014), 669-686.
Orhan S., Demirci, K., Statistical approximation by double sequences of positive linear operators on modular spaces, Positivity 19(2015), 23-36.
Patterson, R.F., Savas, E., Uniformly summable double sequences, Studia Scientiarum Mathematicarum Hungarica 44(2007), 147-158.
Pringsheim, A., Zur theorie der zweifach unendlichen zahlenfolgen, Math. Ann. 53(1900), 289-321.
Sakaoğlu, Ozgüç, İ., Orhan, C., Strong summation process in Lp spaces, Nonlinear Analysis 86(2013), 89-94.
Savaş, E., Rhoades, B.E., Double summability factor theorems and applications, Math. Inequal. Appl. 10(2007), 125-149.
Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2(1951), 73-74.
DOI: http://dx.doi.org/10.24193/subbmath.2018.1.08
Refbacks
- There are currently no refbacks.