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Statistical Deferred Cesàro Summability Mean Based on (pq)-Integers with Application to Approximation Theorems

  • S. K. PaikrayEmail author
  • B. B. Jena
  • U. K. Misra
Chapter

Abstract

This chapter consists of four sections. The first section is introductory in which a concept (presumably new) of statistical deferred Cesàro summability mean based on (pq)-integers has been introduced and accordingly some basic terminologies are presented. In the second section, we have applied our proposed mean under the difference sequence of order r to prove a Korovkin-type approximation theorem for the set of functions 1, \(e^{-x}\) and \(e^{-2x}\) defined on a Banach space \(C[0,\infty )\) and demonstrated that our theorem is a non-trivial extension of some well-known Korovkin-type approximation theorems. In the third 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

Statistical convergence Statistical deferred Cesàro summability Delayed arithmetic mean Difference sequence of order r (p q)-integers Banach space Positive linear operators Korovkin-type approximation theorem Rate of convergence 

2010 Mathematics Subject Classification

Primary 40A05 41A36 Secondary 40G15 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsVeer Surendra Sai University of TechnologyBurlaIndia
  2. 2.Department of MathematicsNational Institute of Science and TechnologyBerhampurIndia

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