Approximation by positive linear operators in modular spaces by power series method

Some Properties of Kantorovich-Stancu-Type Generalization of Szász Operators including Brenke-Type Polynomials via Power Series Summability Method

“…In this paper, we also use the power series summability method which includes several known summability methods such as Abel and Borel (see [2][3][4][5][6][7][8][9]). Note that the power method is more effective than the ordinary convergence (see [10]).…”

Korovkin-type approximation by operators in Riesz spaces via power series method

“…Very recently, in [8] the first author, Dorai and Wójtowicz gave a Riesz space version of the Korovkin theorem. Korovkin-type Approximation theorems have been greatly improved using more general convergences such as statistical, filter convergences and convergences generated by the class of summability methods via power series methods which includes both Abel and Borel methods (see e.g., [9][10][11][12][13][14]). However, in spite of the progress made in the development of the Korovkin-type Approximation theory via power series methods, in the general case of Banach lattices or Riesz spaces it has received little or no attention.…”

“…In fact, this paper is mainly concerned with an abstract version of the Korovkin-type Approximation theorems for a sequence of operators acting on Riesz spaces using summability methods via power series methods. The present paper is largely motivated by the works [10,13]. Actually, Banach lattices and positive operators in [10,13] will be replaced by Riesz spaces and order bounded disjointness preserving operators respectively.…”

“…The present paper is largely motivated by the works [10,13]. Actually, Banach lattices and positive operators in [10,13] will be replaced by Riesz spaces and order bounded disjointness preserving operators respectively. As far as we know, in the literature there are no works fully dedicated to this kind of problems in the framework of Riesz spaces.…”

Approximation of Continuous Periodic Functions of Two Variables via Power Series Methods of Summability

“…Researchers have investigated the approximation of functions in different spaces through various subsets of test functions. Besides, in connection with sequence transformations, weighted mean methods and power series methods of summability have been applied to Korovkin type theorems to recover the convergence of operators for which classical Korovkin theorems fail to work [5,8,11,12,14,15]. Furthermore, there are studies dealing with Korovkin type theorems via weighted mean summability methods for continuous functions of two variables [1,4,6,7].…”