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.
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Paikray, S.K., Jena, B.B., Misra, U.K. (2018). Statistical Deferred Cesàro Summability Mean Based on (p, q)-Integers with Application to Approximation Theorems. In: Mohiuddine, S., Acar, T. (eds) Advances in Summability and Approximation Theory. Springer, Singapore. https://doi.org/10.1007/978-981-13-3077-3_13
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