On convergence in G_Q metric spaces
DOI:
https://doi.org/10.56405/dngcrj.2024.09.01.05Keywords:
statistical convergence, G_{Q}-metric space, Cauchy sequence, quaternion space, triple sequenceAbstract
This paper reviews some basic aspects and proposes and explores the idea of convergence for triple sequences in G_Q-metric space. Furthermore, a thorough analysis and definition of statistical convergence in this context are provided. This link is explored and its ramifications discussed in the last part, which focuses on the relationship between strong summability and the statistical convergence of G_Q-metric spaces.
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Al-Ahmadi, A.M.A. (2017). Quaternion-valued generalized metric spaces and m-quaternion-valued G-isometric mappings. International Journal of Pure and Applied Mathematics, 116 (4), 875-897.
Azam, A., Fisher, B. & Khan, M. (2011). Common fixed point theorems in complex valued metric spaces. Numerical Functional Analysis and Optimization, 32 (3), 243-253.
Choi, H., Kim, S. & Yang, S. (2018). Structure for g-metric spaces and related fixed point theorem. Arxive: 1804.03651v1.
Connor, J. (1988). The statistical and strongly p-Cesàro convergence of sequences. Analysis, 8, 47-63.
El-Sayed Ahmed A., Omran, S. & Asad, A. J. (2014). Fixed point theorems in quaternion-valued metric spaces. Abstract and Applied Analysis, Article ID 258-985, 9 pages, https://doi.org/10.1155/2014/25898.
Farenick, D. R. & Pidkowich, B.A.F. (2003). The spectral theorem in quaternions. Linear Algebra and Applications, 371, 75-102.
Fast, H. (1951). Sur la convergence statistique. Colloquium Mathematicum, 10,142-149.
Fridy, J. A. (1985). On statistical convergence. Analysis, 5, 301-313.
Gürdal, M. (2014). Some types of convergence. Doctoral Dissertation, S. Demirel Univ. Isparta.
Kandemir, H. Şengül, Et, M., & Aral, N. D. (2022). Strongly λ-convergence of order α in Neutrosophic Normed Spaces. Dera Natung Government College Research Journal, 7 (1), 1-9.
Kişi, Ö., Çakal, B. & Gürdal, M. (2024a). Asymptotically lacunary statistical equivalent sequences in a quaternion valued generalized metric spaces, Journal of Applied and Pure Mathematics, in press.
Kişi, Ö., Çakal, B. & Gürdal, M. (2024b). New convergence definitions for sequences in quaternion valued generalized metric spaces. International Journal of Advances in Applied Mathematics and Mechanics, 11 (4), 32-50.
Kişi, Ö., Çakal, B. & Gürdal, M. (2024c). On lacunary I-invariant convergence of sequences in quaternion-valued generalized metric spaces. Journal of Classical Analysis, 24 (2), 111-132.
Kolancı, S. & Gürdal, M. (2023). On ideal convergence in generalized metric spaces. Dera Natung Govt. College Research Journal, 8 (1), 81-96.
Kolancı, S., Gürdal, M. & Kişi, Ö. (2024). On convergence in quaternion-valued g-metric space. Karaelmas Science and Engineering Journal, 14 (3), 106-114.
Mustafa, Z. & Sims, B. (2006). A new approach to generalized metric spaces. Journal of Nonlinear and Convex Analysis, 7 (2), 289-297.
Nabiev, A. A., Savaş, E. & Gürdal, M. (2019). Statistically localized sequences in metric spaces. Journal of Applied Analysis and Computation, 9 (2), 739-746.
Omran, S. & Al-Harthy, S. (2011). On operator algebras over quaternions. International Journal of Mathematical Analysis, 5 (25), 1211-1223.
Şahiner, A., Gürdal, M. & Düden, F.K. (2007). Triple Sequences and their statistical convergence. Selçuk Journal of Applied Mathematics, 8, 49-55.
Temizsu, F. & Et, M. (2023). On deferred f-statistical boundedness. TWMS Journal of Pure Applied Mathematics, 14 (1), 106-119.
Tripathy, B.C. & Et, M. (2005). On generalized difference lacunary statistical convergence. Studia Universitatis Babeş-Bolyai Mathematica, 50 (1), 119-130.
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