ON f−LACUNARY STATISTICAL CONVERGENCE AND STRONG f−LACUNARY SUMMABILITY OF ORDER (α, β)

Authors

  • HACER S¸ENGUL Author

DOI:

https://doi.org/10.5281/7fp1fx48

Abstract

In the paper [37], we introduce the concepts of f−lacunary statistical convergence of order (α, β) and strong f−lacunary summability of order
(α, β) of sequences of real numbers for 0 < α ≤ β ≤ 1, where f is an unbounded modulus and give some inclusion relations between these concepts.
In this paper we continue to examine others relations between f−lacunary
statistical convergence of order (α, β) and strong f−lacunary summability of
order (α, β) for an unbounded modulus f.

References

[1] A. Aizpuru, M. C. List´an-Garc´ıa, F. Rambla-Barreno, Density by moduli and statistical

convergence, Quaest. Math. 37(4) (2014), 525–530.

[2] Y. Altın, Properties of some sets of sequences defined by a modulus function, Acta Math.

Sci. Ser. B Engl. Ed. 29(2) (2009), 427–434.

[3] C. Belen, S. A. Mohiuddine, Generalized weighted statistical convergence and application,

Appl. Math. Comput. 219(18) (2013), 9821–9826.

[4] V. K. Bhardwaj, S. Dhawan, Density by moduli and Wijsman lacunary statistical convergence

of sequences of sets, J. Inequal. Appl. 2017(25) (2017), 20 pp.

[5] V. K Bhardwaj, S. Dhawan, f−statistical convergence of order α and strong Ces`aro summability of order α with respect to a modulus, J. Inequal. Appl. 2015(332) (2015), 14 pp.

[6] N. L. Braha, H. M. Srivastava, S. A. Mohiuddine, A Korovkin’s type approximation theorem

for periodic functions via the statistical summability of the generalized de la Vall´ee Poussin

mean, Appl. Math. Comput. 228 (2014), 162–169.

[7] A. Caserta, Di M. Giuseppe, L. D. R. Koˇcinac, Statistical convergence in function spaces,

Abstr. Appl. Anal. 2011, Art. ID 420419, (2011), 11 pp.

[8] J. S. Connor, The statistical and strong p−Cesaro convergence of sequences, Analysis 8

(1988), 47–63.

[9] H. C¸ akallı, A study on statistical convergence, Funct. Anal. Approx. Comput. 1(2) (2009),

19–24.

[10] M. C¸ ınar, M. Karaka¸s, M. Et, On pointwise and uniform statistical convergence of order α

for sequences of functions, Fixed Point Theory Appl. 2013(33) (2013), 11 pp.

[11] R. C¸ olak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010 (2010), 121–129.

Published

2026-07-18

How to Cite

[1]
HACER S¸ENGULtran. 2026. ON f−LACUNARY STATISTICAL CONVERGENCE AND STRONG f−LACUNARY SUMMABILITY OF ORDER (α, β). Journal of Mathematical Analysis. 15, 01 (Jul. 2026), 40–48. DOI:https://doi.org/10.5281/7fp1fx48.