Rough convergence of sequences in a partial metric space
DOI:
https://doi.org/10.5269/bspm.66978Resumo
In this paper we have studied the notion of rough convergence of sequences in a partial metric space. we have also investigated how far several relevant results on boundedness, rough limit sets etc. which are valid in a metric space are affected in a partial metric space.
Referências
1. S. Aytar, Rough statistical convergence, Numer. Funct. Anal. and Optimiz., 29(3-4), 291-303, (2008).
2. S. Aytar, The rough limit set and the core of a real sequence, Numer. Funct. Anal. and Optimiz., 29(3-4), 283-290, (2008).
3. A. K. Banerjee and A. Dey, Metric Spaces and Complex Analysis, New Age International (P) Limited Publishers, ISBN-10: 81-224-2260-8, ISBN-13: 978-81-224-2260-3, (2008).
4. A. K. Banerjee and R. Mondal, Rough convergence of sequences in a cone metric space, J. Anal., 27, 1179–1188, (2019).
5. D. Bugajewski, P. Mackowiak and R. Wang, On Compactness and Fixed Point Theorems in Partial Metric Spaces, Fixed Point Theory, 23(1), 163-178, (2022).
6. M. Bukatin, R. Kopperman, S. Matthews and H. Pajoohesh, Partial metric spaces, Am. Math. Mon., 116, 708-718 (2009).
7. S. Debnath and D. Rakshit, Rough convergence in metric spaces, Birkhauser, cham, (2017).
8. Huang Long-Gung and Zhang X, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. and Appl., 332(2), 1468-1476, (2007).
9. P. Malik and M. Maity, On rough convergence of double sequence in normed linear spaces, Bull. Allah. Math. Soc., 28(1), 89-99, (2013).
10. P. Malik and M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afr. Mat., 27, 141-148, (2016).
11. R. Mondal, Rough Cauchy sequences in a cone metric space, J. Math. Comput. Sci., 12 (2022), Article ID 14.
12. S. Matthews, Partial metric topology, In: Proceedings of the 8th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, 728, 183-197, (1994).
13. H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. and Optimiz., 22(1-2), 199-222, (2001).
14. H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. and Optimiz., 24(3-4), 285-301, (2003).
2. S. Aytar, The rough limit set and the core of a real sequence, Numer. Funct. Anal. and Optimiz., 29(3-4), 283-290, (2008).
3. A. K. Banerjee and A. Dey, Metric Spaces and Complex Analysis, New Age International (P) Limited Publishers, ISBN-10: 81-224-2260-8, ISBN-13: 978-81-224-2260-3, (2008).
4. A. K. Banerjee and R. Mondal, Rough convergence of sequences in a cone metric space, J. Anal., 27, 1179–1188, (2019).
5. D. Bugajewski, P. Mackowiak and R. Wang, On Compactness and Fixed Point Theorems in Partial Metric Spaces, Fixed Point Theory, 23(1), 163-178, (2022).
6. M. Bukatin, R. Kopperman, S. Matthews and H. Pajoohesh, Partial metric spaces, Am. Math. Mon., 116, 708-718 (2009).
7. S. Debnath and D. Rakshit, Rough convergence in metric spaces, Birkhauser, cham, (2017).
8. Huang Long-Gung and Zhang X, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. and Appl., 332(2), 1468-1476, (2007).
9. P. Malik and M. Maity, On rough convergence of double sequence in normed linear spaces, Bull. Allah. Math. Soc., 28(1), 89-99, (2013).
10. P. Malik and M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afr. Mat., 27, 141-148, (2016).
11. R. Mondal, Rough Cauchy sequences in a cone metric space, J. Math. Comput. Sci., 12 (2022), Article ID 14.
12. S. Matthews, Partial metric topology, In: Proceedings of the 8th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, 728, 183-197, (1994).
13. H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. and Optimiz., 22(1-2), 199-222, (2001).
14. H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. and Optimiz., 24(3-4), 285-301, (2003).
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2025-07-13
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