A-Statistical Supremum-Infimum and A-Statistical Convergence

In this paper, the concept of A-statistical supremum (sup A x) and A-statistical infumum (inf A x) for real valued sequences x = (x n ) are defined and studied. It is mainly shown that, the equality of supA x and inf A x is necessary but not sufficient for to existence of usual limit of the sequence. On the other hand, the equality of sup A x and inf A x is necessary and sufficient for to existence of A-statistical limit of the real valued sequences.