A Study on Lacunary Strong Convergence according to Modulus Functions

Authors

  • Mustafa I. Hatim Department of Mathematics, Firat University, Turkey
  • Çiğdem A. Bektaş Department of Mathematics, Firat University, Turkey

DOI:

https://doi.org/10.7546/CRABS.2023.10.01

Keywords:

sequence space, modulus function, lacunary sequence, strong convergence, statistical convergence

Abstract

In this article, we study a new generalization of the lacunary strongly convergent sequences and introduce the concept of lacunary strong convergence according to $$g^k$$ for sequences of complex (or real) numbers, where $$g^k=g\circ g\circ\dots\circ g$$ ($$k$$ times) represents a composite modulus function. After that, we determine the connections of lacunary strong convergence and lacunary statistical convergence to lacunary strong convergence according to $$g^k$$. Furthermore, we investigate several properties of this generalization.

Author Biographies

Mustafa I. Hatim, Department of Mathematics, Firat University, Turkey

Mailing Address:
Department of Mathematics,
Firat University
23119 Elazig, Turkey

E-mail: mustafa.ih88@gmail.com

Çiğdem A. Bektaş, Department of Mathematics, Firat University, Turkey

Mailing Address:
Department of Mathematics,
Firat University
23119 Elazig, Turkey

E-mail: cbektas@firat.edu.tr

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Published

31-10-2023

How to Cite

[1]
M. Hatim and Çiğdem Bektaş, “A Study on Lacunary Strong Convergence according to Modulus Functions”, C. R. Acad. Bulg. Sci., vol. 76, no. 10, pp. 1475–1485, Oct. 2023.

Issue

Section

Mathematics