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

S. K. Paikray (), B. B. Jena () and U. K. Misra ()
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S. K. Paikray: Veer Surendra Sai University of Technology, Department of Mathematics
B. B. Jena: Veer Surendra Sai University of Technology, Department of Mathematics
U. K. Misra: National Institute of Science and Technology, Department of Mathematics

A chapter in Advances in Summability and Approximation Theory, 2018, pp 203-222 from Springer

Abstract: 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 (p, q)-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; Primary 40A05; 41A36; Secondary 40G15 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-981-13-3077-3_13

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