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Öğe Approximation via Statistical Convergence in the Sense of Power Series Method of Bogel-Type Continuous Functions(Maik Nauka/Interperiodica/Springer, 2022) Demirci, K.; Yildiz, S.; Dirik, F.In this paper, we study Korovkin-type approximation for double sequences of positive linear operators defined on the space of all real valued B-continuous functions via the notion of statistical convergence in the sense of power series methods instead of Pringsheim convergence.We present an interesting application that satisfies our new approximation theorem which wasn'tsatisfied the one studied before. In addition, we derive the rate of convergence of the proposed approximation theorem. Finally, we give a conclusion for periodic functions.Öğe I-convergence of positive linear operators on Lp weighted spaces(Eudoxus Press, Llc, 2008) Dirik, F.; Aral, A.; Demirci, K.In this paper, using the concept of I-convergence we prove a Korovkin type approximation by means of positive linear operators defined on the weighted space L-p,L-w(R). Also we state its n-dimensional analogue for the weighted space L-p,L-Omega(R-n). Also we display an example such that our method of convergence is stronger than the usual convergence in the weighted spaces L-p,L-w(R) and L-p,L-Omega(R-n).
