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Öğe A Korovkin-type theorem for double sequences of positive linear operators via power series method(Springer, 2018) Sahin, Pinar Okcu; Dirik, FadimeIn this paper, using power series method we obtain a Korovkin type theorem for double sequences of real valued functions defined on a compact subset of (the real two-dimensional space). We also present an example that satisfies our theorem. Finally, we calculate the rate of convergence.Öğe Statistical equi-equal convergence of positive linear operators(Springer, 2019) Dirik, Fadime; Sahin, Pinar OkcuMany researchers have been interested in the concept of statistical convergence because of the fact that it is stronger than the classical convergence. Also, the concepts of statistical equal convergence and equi-statistical convergence are more general than the statistical uniform convergence. In this paper we define a new type of statistical convergence by using the notions of equi-statistical convergence and statistical equal convergence to prove a Korovkin type theorem. We show that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were demonstrated by earlier authors. After, we present an example in support of our definition and result presented in this paper. Finally, we also compute the rates of statistical equi-equal convergence of sequences of positive linear operators.Öğe Statistical Relative Equal Convergence Of Double Function Sequences And Korovkin-Type Approximation Theorem(Tsing Hua Univ, Dept Mathematics, 2019) Sahin, Pinar Okcu; Dirik, FadimeIn this work, we introduce our new concept of the statistical equal convergence for double function sequences. Later, we introduce the concept of statistical relative equal convergence of double function sequences which is stronger than the notion of statistical relative convergence and statistical uniform convergence to demonstrate a Korovkin type approximation theorem and prove that our theorem is a non-trivial extension of some well-known Korovkin type approximation theorems which were proven by earlier authors. We present an example in support of our definition and result presented in this paper. Finally, we study Voronovskaya type theorem via statistical relative equal convergence.Öğe Statistical Relative Uniform Convergence Of Double Sequences Of Positive Linear Operators(Tsing Hua Univ, Dept Mathematics, 2017) Sahin, Pinar Okcu; Dirik, FadimeIn the present paper, we introduce the concept of A-statistical relative uniform convergence for double sequences of functions dened on a compact subset of the real two-dimensional space. Based upon this denition, we prove Korovkin-type approximation theorem. Finally, we compute the rate of convergence.Öğe Statistical Relatively Equal Convergence and Korovkin-Type Approximation Theorem(Springer Basel Ag, 2017) Dirik, Fadime; Sahin, Pinar OkcuIn the present work, we define a new type of statistical convergence by using the notion of the relatively uniform convergence. We prove a Korovkin-type approximation theorem with the help of this new definition. Then, we construct a strong example that satisfies our theory. Finally, we compute the rate of statistical relatively equal convergence.
