Characterization of rough weighted statistical limit set

Abstract

Abstract Our focus is to generalize the definition of the weighted statistical convergence in a wider range of the weighted sequence {tn } n∈ℕ. We extend the concept of weighted statistical convergence and rough statistical convergence to renovate a new concept namely, rough weighted statistical convergence. On a continuation we also define rough weighted statistical limit set. In the year (2008) Aytar established the following results: The diameter of rough statistical limit set of a real sequence is ≤ 2r (where r is the degree of roughness) and in general it has no smaller bound. If the rough statistical limit set is non-empty then the sequence is statistically bounded. If x ∗ and c belong to rough statistical limit set and statistical cluster point set respectively, then |x ∗ − c| ≤ r. We investigate whether the above mentioned three results are satisfied for rough weighted statistical limit set or not? Answer is no. So our main objective is to interpret above mentioned different behaviors of the new convergence and characterize the rough weighted statistical limit set. Also we show that this set satisfies some topological properties like boundedness, compactness, path connectedness etc.