On Certain Statistical Convergence Criteria for Martingale Sequences via Deferred Ces`aro Mean with Some Applications

Authors

  • Hemen Dutta Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
  • Bidu Bhusan Jena Faculty of Science (Mathematics), Sri Sri University, Cuttack 754006, Odisha, India
  • Narayan Prasad Pahari Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu, Nepal
  • Susanta Kumar Paikray Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India

DOI:

https://doi.org/10.3126/jnms.v7i1.67486

Keywords:

Stochastic sequences, Martingale sequences, Statistical uniform integrable, , Statistical uniform integrable, Deferred Ces`aro mean, Banach space, Korovkin-type theorem

Abstract

In this paper, we investigate and study various new notions of statistical convergence criteria of martingale sequences via deferred Ces`aro mean. We then establish several results concerning the relation among these beautiful and potentially useful concepts. Moreover, our proposed techniques contributed to finding several new approximation results of the Korovkin-type for martingale sequences over complete normed linear spaces. We also present some concrete examples to establish the stronger side of our results.

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Published

2024-07-04

How to Cite

Dutta, H., Jena, B. B., Pahari, N. P., & Paikray, S. K. (2024). On Certain Statistical Convergence Criteria for Martingale Sequences via Deferred Ces`aro Mean with Some Applications. Journal of Nepal Mathematical Society, 7(1), 40–60. https://doi.org/10.3126/jnms.v7i1.67486

Issue

Vol. 7 No. 1 (2024)

Section

Articles

License

© Nepal Mathematical Society