A certain class of equi-statistical convergence in the sense of the deferred power-series method

Srivastava, Hari MohanJena, Bidu BhusanPaikray, Susanta Kumar2024-01-042024-01-0420232023Srivastava, H. M., Jena, B. B., & Paikray, S. K. (2023). A certain class of equi-statistical convergence in the sense of the deferred power-series method. Axioms, 12(10), 964. https://doi.org/10.3390/axioms12100964https://doi.org/10.3390/axioms12100964http://hdl.handle.net/1828/15786In this paper, we expose the ideas of point-wise statistical convergence, equi-statistical convergence and uniform statistical convergence in the sense of the deferred power-series method. We then propose a relation connecting them, which is followed by several illustrative examples. Moreover, as an application viewpoint, we establish an approximation theorem based upon our proposed method for equi-statistical convergence of sequences of positive linear operators. Finally, we estimate the equi-statistical rates of convergence for the effectiveness of the results presented in our study.enAttribution 2.5 Canadastatistical convergencedeferred power-series methodCesàro summabilityKorovkin-type theorembernstein polynomialsrate of convergenceA certain class of equi-statistical convergence in the sense of the deferred power-series methodArticleDepartment of Mathematics and Statistics