A variation on Abel statistical ward continuity

Abel statistical quasi Cauchy sequences

“…A and ∆A will denote the set of Abel convergent sequences and the set of Abel quasi Cauchy sequences, respectively. Recently the concept of Abel statistical convergence of a sequence is investigated in [34] (see also [20]) in the sense that a sequence (α k ) is called Abel statistically convergent to a real number L if…”

“…The analogous property fails for Abel statistical quasi Cauchy sequences. A counter example is the sequence ( √ k) with the subsequence (k) ( [20]). Any convergent sequence is Abel statistically quasi Cauchy: let (α k ) be a convergent sequence with limit L, and…”

“…We acknowledge that some of the results in this paper were presented at the International Conference on Advancements in Mathematical Sciences in 2015, appeared in Proceedings of the conference ( [20]).…”

Beyond cauchy and quasi-Cauchy sequences

“…Recently, using the idea of continuity of a real function in terms of sequences, many kinds of continuities were introduced and investigated, not all but some of them we recall in the following: slowly oscillating continuity ( [39]), quasi-slowly oscillating continuity ( [26]), ward continuity ( [7]), statistical ward continuity ( [9]), λ-statistically ward continuity ( [22]), ρ-statistical ward continuity ( [4]), ideal ward continuity ( [17]), Abel statistical continuity ( [24]), strongly lacunary-ward continuity ( [18]), lacunary statistical ward continuity ( [15]), and arithmetic continuity ( [6,40]). Investigation of some of these kinds of continuities lead some authors to enable interesting results related to uniform continuity of a real function in terms of sequences in the above manner ([9, Theorem 6], [39,Theorem 8], [26,Theorem 2.3], [7,Theorem 7], [1,Theorem 1], [2,Theorem 3.8], [22,Corollary 6]).…”