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

In this paper we prove an Ozguç, Yurdakadim and Taş version of the Korovkin-type approximation by operators in the sense of the power series method. That is, we try to extend the Korovkin approximation theorems, obtained by Ozguç and Taş in 2016, and Taş and Yurdakadim in 2017, for concrete classes of Banach spaces to the class of Riesz spaces. Some applications are presented.

On Some Statistical Approximation by (p,q)-Bleimann, Butzer and Hahn Operators

In this article, we propose a different generalization of ( p , q ) -BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where ( p , q ) -integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators.

Korovkin Approximation Theorem with Ω Striped

In this paper, we discuss some theorem reached M. Mursaleen, there are several properties of statistical lacunary summability presented (Mursaleen, M. & Alotaibi,A., 2011; Mursaleen, M. &Alotaibi, A., 2011; Edely, O. H. & Mursaleen, M., 2009). This is concerned the motivate to narrowly delineated context denoted by Ω striped usage in prove our theorem (theorem A). We introduce some piecewise polynomial functions (Kopotun,K. A., 2006) and some results Korovkin theorem.