αβ− Statistical Convergence

ABSTRACT: In this thesis we studied αβ-statistical convergence. We started with the discussion of statistical convergence. Later, we gave a brief summary of λ-statistical, lacunary statistical and A−statistical convergences. The concept of αβ-statistical convergence which is the main interest of this thesis has been considered in the last chapter of the thesis. In this chapter we also show that αβ-statistical convergence is a non-trivial extension of statistical, λ-statistical and lacunary statistical convergences. Finally, we introduced boundedness of a sequence in the sense of αβ-statistical convergence. Keywords: αβ−Statistical Convergence, λ−Statistical Convergence, Statistical Convergence, A-Statistical Convergence. …………………………………………………………………………………………………………………………