On statistical deferred cesàro summability

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, e−x, 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.