A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces-Reference-Cited by-同舟云学术

A new notion of convergence defined by weak Fibonacci lacunary statistical convergence in normed spaces

Published:2024-08-03 Issue: Volume: Page:
ISSN:1425-6908
Container-title:Journal of Applied Analysis
language:en
Short-container-title:

Author:

Ibrahim Ibrahim S.¹^ORCID,Listán-García María C.²,Colak Rifat³

Affiliation:

1. Department of Mathematics , College of Education , 557749 University of Zakho , Zakho , Iraq

2. Department of Mathematics , Faculty of Science , University of Cádiz , Cádiz , Spain

3. Department of Mathematics , Faculty of Science , Firat University , Elazig , Türkiye

Abstract

Abstract The applications of a Fibonacci sequence in mathematics extend far beyond their initial discovery and theoretical significance. The Fibonacci sequence proves to be a versatile tool with real-world implications and the practical utility of manifests in various fields, including optimization algorithms, computer science and finance. In this research paper, we introduce new versions of convergence and summability of sequences in normed spaces with the help of the Fibonacci sequence called weak Fibonacci φ-lacunary statistical convergence and weak Fibonacci φ-lacunary summability, where φ is a modulus function under certain conditions. Furthermore, we obtain some relations related to these concepts in normed spaces.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/jaa-2023-0166/pdf

Reference44 articles.

1. B. Altay, F. J. García-Pacheco and R. Kama, On f-strongly Cesàro and f-statistical derivable functions, AIMS Math. 7 (2022), no. 6, 11276–11291.

2. N. D. Aral and H. Şengül Kandemir, On f-lacunary statistical convergence of order β of double sequences for difference sequences of fractional order, Facta Univ. Ser. Math. Inform. 38 (2023), no. 2, 329–343.

3. V. K. Bhardwaj and S. Dhawan, Korovkin type approximation theorems via f-statistical convergence, J. Math. Anal. 9 (2018), no. 2, 99–117.

4. M. Candan, Some characteristics of matrix operators on generalized Fibonacci weighted difference sequence space, Symmetry 14 (2022), no. 7, Article ID 1283.

5. M. Candan and K. Kuddusi, Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, British J. Math. Comp. Sci. 7 (2015), no. 2, 150–167.