Journal of Applied Mathematics and Computing https://doi.org/10.1007/s12190-020-01398-5 ORIGINAL RESEARCH Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems Naim L. Braha 1 · H. M. Srivastava 2,3 · Mikail Et 4 Received: 18 May 2020 / Revised: 3 July 2020 / Accepted: 6 July 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020 Abstract In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem. Keywords Weighted statistical convergence · Sequence spaces · Korovkin type theorem · Rate of convergence · Voronovskaya type theorem Mathematics Subject Classification 40G15 · 41A36 · 46A35 · 46A45 1 Introduction We shall denote by N the set of all natural numbers. Let K ∈ N and let K n ={k ≤ n : k ∈ K }. Then the natural density of K is defined by d ( K ) = lim n→∞ | K n | n if the limit exists, where the vertical bars in | K n | indicate the number of elements in the enclosed B Naim L. Braha nbraha@yahoo.com H. M. Srivastava harimsri@math.uvic.ca Mikail Et mikailet68@gmail.com 1 Department of Mathematics and Computer Sciences, University of Prishtina, Avenue Mother Teresa, No-5, 10000 Pristina, Kosova 2 Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada 3 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China 4 Department of Mathematics, Fırat University, 23119 Elazig, Turkey 123