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On Statistical Deferred Cesàro Summability

  • Hemen Dutta
  • S. K. PaikrayEmail author
  • B. B. Jena
Chapter

Abstract

This chapter consists of five sections. The first section is introductory, where from the concept of infiniteness to the development of summability methods are presented. In the second section, ordinary and statistical versions of Cesàro and deferred Cesàro summability methods have been introduced and accordingly some basic terminologies are considered. In the third section, we have applied our proposed deferred Cesàro mean to prove a Korovkin-type approximation theorem for the set of functions 1, ex, and e−2x defined on a Banach space and demonstrated that our theorem is a non-trivial extension of some well-known Korovkin-type approximation theorems. In the fourth section, we have established a result for the rate of our statistical deferred Cesàro summability mean with the help of the modulus of continuity. Finally, in the last section, we have given some concluding remarks and presented some interesting examples in support of our definitions and results.

Keywords

Infinite series Natural density Statistical convergence Statistical deferred Cesàro convergence Statistical deferred Cesàro summability Korovkin-type approximation theorem Modulus of continuity Rate of statistical deferred Cesàro summability 

Notes

Acknowledgements

The authors would like to express their heartfelt thanks to the editors and anonymous referees for their most valuable comments and constructive suggestions which leads to the significant improvement of the earlier version of the manuscript.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsGauhati UniversityGuwahatiIndia
  2. 2.Department of MathematicsVeer Surendra Sai University of TechnologyBurlaIndia

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