Effects on rough I-convergence to induce the weighted sequence

Abstract

Two classes of sets are introduced: rough weighted I-lacunary statistical limit set and weighted I-lacunary statistical cluster points set which are natural generalizations of rough I-limit set and I-cluster points set respectively. Some examples are constructed to ensure the deviation of basic results. So our aim is to analyze the different behaviors of the new convergences and characterize both the sets in topological approach like closedness, boundedness, compactness etc.