Abstract
In this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method. Then, we also present theorems of Korovkin-type via statistical relative A-summation process via power series method on modular spaces, including as particular cases weighted spaces, certain interpolation spaces, Orlicz and Musielak-Orlicz spaces, Lp spaces and many others. Later, we consider some application to Kantorovich-type operators in Orlicz spaces. Moreover, we present some estimates of rates of convergence via modulus of continuity. We end the paper with giving some concluding remarks.
Publisher
Sinop Universitesi Fen Bilimleri Dergisi
Reference42 articles.
1. Niven, I., Zuckerman, H. S., & Montgomery, H. L. (1991). An introduction to the theory of numbers. John Wiley & Sons.
2. Fast, H. (1951). Sur la convergence statistique. Colloquium mathematicae, 2(3-4), 241-244.
3. Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique. Colloquium mathematicae, 2(1), 73-74.
4. Ünver, M., & Orhan, C. (2019). Statistical convergence with respect to power series methods and applications to approximation theory. Numerical Functional Analysis and Optimization, 40(5), 535-547. https://doi.org/10.1080/01630563.2018.1561467
5. Kratz, W., & Stadtmüller, U. (1989). Tauberian theorems for Jp-summability. Journal of mathematical analysis and applications, 139(2), 362-371. https://doi.org/10.1016/0022-247X(89)90113-3
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献