Where and are the sequences of nonnegative integers satisfying Now is the time to recall the key notions of our study deferred Cesàro mean and deferred statistical convergence.ĭeferred Cesàro mean, defined by Agnew in 1932, is a generalization of Cesàro mean, and its definition can be given as follows: In recent years, researchers have attempted to apply the relationship between statistical convergence and summability theory in applicable disciplines. Over the years, that notion has been presented in a variety of ways, and its relationship to aggregation has been investigated in several domains. Provided that limit exists, where is the characteristic function of Ifįor each, then is said to be statistically convergent to writing. The natural density of a subset of is defined as , and this concept has been extended to sequence spaces, accordingly, to the notions such as summability theory. (), Kucukaslan and Yılmazturk (), Šalát, Ercan et al. (), Çolak, Connor, Fridy, Altay et al. The concept was later applied to summability theory by various authors such as Çinar et al. Then, it has been addressed under various titles including Fourier analysis, Ergodic theory, Number theory, Turnpike theory, Measure theory, Trigonometric series, and Banach spaces. In 1935, Zygmund introduced the concept of statistical convergence to the mathematical community, Steinhaus and Fast independently introduced the concept of statistical convergence, and Schoenberg reintroduced it in the year 1959.
One of these ideas is the converging statistics. Many types of convergence have been defined so far, and then, very valuable results and concepts have been presented to the mathematical community. This concept has been studied theoretically by many mathematicians in many different fields. In mathematics, the concept of convergence has been of great importance for many years. In this paper, we introduce the concepts of deferred statistical convergence of order and strongly deferred Cesàro summable functions (real valued) of order on time scales and give some relationships between deferred statistical convergence of order and strongly deferred Cesàro summable functions (real valued) of order on time scales.
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