### WEIGHTED STATISTICAL CONVERGENCE OF ORDER ALPHA OF DIFFERENCE SEQUENCES

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#### Abstract

Study of difference sequences is a recent development in the summability theory. Sometimes a situation may arise that we have a sequence at hand and we are interested in sequences formed by its successive differences and in the structure of these new sequences. Studies on difference sequences were introduced in the 1980s and after that many mathematicians studied these kind of sequences and obtained some generalized difference sequence spaces. In this study, we generalize the concepts of weighted statistical convergence and weighted $\overline{\left[ N_{p}\right] }-$summability of real (or complex) numbers sequences to the concepts of $\Delta^{m}-$weighted statistical convergence of order $\alpha$ and weighted $\left[ \overline{N_{p}}^{\alpha}\right] \left(\Delta^{m},r\right)-$summability of order $\alpha$ by using generalized difference operator $\Delta^{m}$ and examine the relationships between $\Delta^{m}-$weighted statistical convergence of order $\alpha$ and weighted $\left[ \overline {N_{p}}^{\alpha}\right] \left( \Delta^{m},r\right) -$summability of order $\alpha.$ Our results are more general than the corresponding results in the existing literature.

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DOI: https://doi.org/10.22190/FUMI211004022S

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