Ward Continuity in Topological Vector Spaces
DOI:
https://doi.org/10.5269/bspm.81376Resumo
In this paper, we investigate the concepts of quasi-Cauchyness of sequences and ward continuity of functions in topological vector spaces. We prove that totally boundedness is equivalent to ward compactness and ward continuity on a totally bounded subset $E$ of topological vector space $X$ coincides with uniform continuity. We also prove some other interesting theorems.
Referências
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https://doi.org/10.2298/FIL1305925C
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2 (2017), 313-321.
20. Fikriye Ince Dagci, Huseyin Cakalli; On variations on quasi Cauchy sequences in metric spaces. AIP Conf. Proc. 2 April
2019; 2086 (1): 030012. https://doi.org/10.1063/1.5095097
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0354-5180. https://doi.org/10.2298/FIL2425917D
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Corp., New York, 2012 (2012), Article ID 497594 6 pages. http://www.hindawi.com/journals/aaa/2012/497594/cta/
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23. S. Ersan and H. Cakalli, Ward Continuity in 2-Normed Spaces, Filomat 29 7 (2015), 1507-1513. DOI
10.2298/FIL1507507E
24. Ljubisa D.R. Kocinac, Selection properties in fuzzy metric spaces, Filomat. 26 2 (2012), 305-312.
https://doi.org/10.2298/FIL1202305K
25. R.F. Patterson and H. Cakalli, Quasi Cauchy double sequences, Tbilisi Mathematical Journal 8 2 (2015),
211-219. https://projecteuclid.org/journals/tbilisi-mathematical-journal/volume-8/issue-2/Quasi-Cauchy-double-
sequences/10.1515/tmj-2015-0023.pdf
26. R.W. Vallin, Creating slowly oscillating sequences and slowly oscillating continuous functions (with an appendix by
Vallin and H. C¸ akallı, Acta Math. Univ. Comenianae 25 (2011), 71-78.
Appl. Sci. 44 9 (2021) 7834-7844. https://doi.org/10.1002/mma.7113
2. C.G. Aras, A. Sonmez, H. Cakalli, An approach to soft functions, J. Math. Anal. 8, 2, 129-138, (2017)
3. D. Burton, and J. Coleman, Quasi-Cauchy Sequences, Amer. Math. Monthly. 117 4 (2010), 328-333.
https://doi.org/10.4169/000298910X480793
4. H. Cakalli, A Variation on Statistical Ward Continuity. Bull. Malays. Math. Sci. Soc. 40 (2017), 1701–1710.
https://doi.org/10.1007/s40840-015-0195-0 .
5. H. Cakalli, Variations on statistical quasi Cauchy sequences, Bol. Soc. Paran. Mat. (3s.) 26 2 (2019), 1-10.
https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/download/39991/751375146545/
6. H. Cakalli, C.G. Aras, A. Sonmez, Lacunary statistical ward continuity, AIP Conf. Proc. 1676, 2015 020042
https://doi.org/10.1063/1.4930468
7. H Cakalli and R.F. Patterson, Functions preserving slowly oscillating double sequences, An. Stiint. Univ. Al. I. Cuza
Iasi. Mat. (N.S.) 62 1,2 (2016), 531-536.
8. Huseyin Cakalli, Yasemin Simsek; Quasi Cauchy sequences in topological vector spaces. AIP Conf. Proc. 4 August 2025;
3431 (1): 020004. https://doi.org/10.1063/5.0290216
9. I. Canak and M. Dik, New types of continuities, Abstr. Appl. Anal. 2010 (2010) Article ID 258980, 6 pages.
https://doi.org/10.1155/2010/258980
10. A. Coskun, C. Aras, H. Cakalli, A. Sonmez, ”Soft matrices on soft multisets in an optimal decision process,” 3rd
International Conference on Analysis and Applied Mathematics (ICAAM) , vol.1759, Almaty, Kazakhstan, 2016
11. H.C¸ akallı, Forward compactness, Conference on Summability and Applications, Shawnee State University, November
6-November 8, (2009). ttps://webpages.math.luc.edu/ mgb/ShawneeConference/Articles/HuseyinCakalliOhio.pdf .
12. H. C¸ akallı, Forward continuity, J. Comput. Anal. Appl. 13 2 (2011), 225-230.
13. H. C¸ akalli, Slowly oscillating continuity, Abstr. Appl. Anal. 2008 (2008) Article ID 485706 5 pages.
https://doi.org/10.1155/2008/485706
14. H. C¸ akalli, Statistical ward continuity. Appl. Math. Lett. 24 (2011), 1724-1728.
https://doi.org/10.1016/j.aml.2011.04.029
15. H. C¸ akalli, Statistical-quasi-Cauchy sequences, Math. Comput. Modelling 54 (2011), 1620-1624.
https://doi.org/10.1016/j.mcm.2011.04.037
16. H. C¸ akalli, A new approach to statistically quasi Cauchy sequences, Maltepe J. Math., 1 1 (2019), 1-8.
https://dergipark.org.tr/en/pub/mjm/issue/41581/477328
17. H. C¸ akalli, and Pratulananda Das, Fuzzy compactness via summability, Appl. Math. Lett. 22 (2009), 1665-1669.
https://doi.org/10.1016/j.aml.2009.05.015
18. H. C¸ akalli and A. Sonmez, Slowly oscillating continuity in abstract metric spaces, Filomat 27 (2013), 925-930.
https://doi.org/10.2298/FIL1305925C
19. H. C¸ akalli, A. Sonmez, and C.G. Aras, λ-statistical ward continuity, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 63
2 (2017), 313-321.
20. Fikriye Ince Dagci, Huseyin Cakalli; On variations on quasi Cauchy sequences in metric spaces. AIP Conf. Proc. 2 April
2019; 2086 (1): 030012. https://doi.org/10.1063/1.5095097
21. F. Ince Da˘gcı and H. Cakalli, Quasi-Cauchy sequences on asymmetric metric spaces, Filomat 38 1–7 (2024), ISSN
0354-5180. https://doi.org/10.2298/FIL2425917D
22. D. Djurcic, Ljubisa D. R. Kocinac, M. R. Zizovic, Double Sequences and Selections, Abstr. Appl. Anal. Hindawi Publ.
Corp., New York, 2012 (2012), Article ID 497594 6 pages. http://www.hindawi.com/journals/aaa/2012/497594/cta/
https://doi.org/10.1155/2012/497594.
23. S. Ersan and H. Cakalli, Ward Continuity in 2-Normed Spaces, Filomat 29 7 (2015), 1507-1513. DOI
10.2298/FIL1507507E
24. Ljubisa D.R. Kocinac, Selection properties in fuzzy metric spaces, Filomat. 26 2 (2012), 305-312.
https://doi.org/10.2298/FIL1202305K
25. R.F. Patterson and H. Cakalli, Quasi Cauchy double sequences, Tbilisi Mathematical Journal 8 2 (2015),
211-219. https://projecteuclid.org/journals/tbilisi-mathematical-journal/volume-8/issue-2/Quasi-Cauchy-double-
sequences/10.1515/tmj-2015-0023.pdf
26. R.W. Vallin, Creating slowly oscillating sequences and slowly oscillating continuous functions (with an appendix by
Vallin and H. C¸ akallı, Acta Math. Univ. Comenianae 25 (2011), 71-78.
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Publicado
2026-06-05
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Conf. Issue: Advances in Mathematical Sciences
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