"lambda" - STATISTICAL SUPREMUM - INFIMUM AND "lambda" - STATISTICAL CONVERGENCE

Abstract

Convergence of real valued sequences especially statistical convergence is very popular subject in Mathematical Analysis. Also, it has got a lot of characterizations in literature. In this paper, we are going to define $\lambda$-statistical supremum and $\lambda$-statistical infimum for real valued sequence $x=(x_n)$. After giving some basic properties of these new notations, then we are going to find a necessary and sufficient condition for to existence of λ-statistical convergence of the sequence $x=(x_n)$.