On $\theta(\tau_1,\tau_2)p$-Open Functions and $\theta(\tau_1,\tau_2)p$-Closed Functions

Srisarakham, Napassanan; Sama-Ae, Areeyuth; Boonpok, Chawalit

doi:10.28924/2291-8639-23-2025-249

Research Article

On $\theta(\tau_1,\tau_2)p$-Open Functions and $\theta(\tau_1,\tau_2)p$-Closed Functions

Napassanan Srisarakham
Areeyuth Sama-Ae
Chawalit Boonpok*

* Corresponding author

Abstract

This paper deals with the concepts of $\theta(\tau_1,\tau_2)p$-open functions and $\theta(\tau_1,\tau_2)p$-closed functions. Moreover, several characterizations and some properties concerning $\theta(\tau_1,\tau_2)p$-open functions and $\theta(\tau_1,\tau_2)p$-closed functions are considered.

How to Cite

N. Srisarakham, A. Sama-Ae, C. Boonpok, On $\theta(\tau_1,\tau_2)p$-Open Functions and $\theta(\tau_1,\tau_2)p$-Closed Functions, Int. J. Anal. Appl. 23 (2025), 249. https://doi.org/10.28924/2291-8639-23-2025-249

BibTeX

@article{Srisarakham2025,
  author  = {Srisarakham, Napassanan and Sama-Ae, Areeyuth and Boonpok, Chawalit},
  title   = {On \(\theta(\tau_1,\tau_2)p\)-Open Functions and \(\theta(\tau_1,\tau_2)p\)-Closed Functions},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {249},
  doi     = {10.28924/2291-8639-23-2025-249}
}

References

[1] M.E. Abd El-Monsef, S.N. El-Deeb, R.A. Mahmoud, $\beta$-Open Sets and $\beta$-Continuous Mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
[2] C. Boonpok, P. Pue-on, Weakly $\theta s(\Lambda,p)$-open functions and weakly $\theta s(\Lambda,p)$-closed functions, Asia Pac. J. Math. 11 (2024), 13. https://doi.org/10.28924/APJM/11-13.
[3] C. Boonpok, M. Thongmoon, Weakly $p(\Lambda,p)$-Open Functions and Weakly $p(\Lambda,p)$-Closed Functions, Int. J. Ana. Appl. 22 (2024), 10. https://doi.org/10.28924/2291-8639-22-2024-10.
[4] C. Boonpok, M. Thongmoon, Properties of Weakly $\beta(\Lambda,p)$-Open Functions and Weakly $\beta(\Lambda,p)$-Closed Functions, Eur. J. Pure Appl. Math. 17 (2024), 248–255. https://doi.org/10.29020/nybg.ejpam.v17i1.4974.
[5] C. Boonpok, N. Srisarakham, $\theta p(\Lambda,p)$-Open Functions and $\theta p(\Lambda,p)$-Closed Functions, Asia Pac. J. Math. 10 (2023), 48. https://doi.org/10.28924/APJM/10-48.
[6] C. Boonpok, $(\tau_1,\tau_2)\delta$-Semicontinuous Multifunctions, Heliyon, 6 (2020), e05367. https://doi.org/10.1016/j.heliyon.2020.e05367.
[7] C. Boonpok, C. Viriyapong, M. Thongmoon, on Upper and Lower $(\tau_1,\tau_2)$-Precontinuous Multifunctions, J. Math. Computer Sci. 18 (2018), 282–293. https://doi.org/10.22436/jmcs.018.03.04.
[8] C. Boonpok, Weakly Open Functions on Bigeneralized Topological Spaces, Int. J. Math. Anal. 4 (2010), 891–897.
[9] M. Caldas, S. Jafari, G. Navalagi, T. Noiri, On Pre-$\theta$-Open Sets and Two Classes of Functions, Bull. Iran. Math. Soc. 32 (2006), 47–65.
[10] M. Caldas, G. Navalagi, On Weak Forms of Semi-Open and Semi-Closed Functions, Missouri J. Math. Sci. 18 (2006), 165–178.
[11] M. Caldas, G. Navalagi, On Weak Forms of Preopen and Preclosed Functions, Arch. Math. 40 (2004), 119–128. http://dml.cz/dmlcz/107896.
[12] M. Chiangpradit, S. Sompong, C. Boonpok, On Characterizations of $(\tau_1,\tau_2)$-Regular Spaces, Int. J. Math. Comput. Sci. 19 (2024), 1329–1334.
[13] N. Chutiman, C. Boonpok, Some Properties of Weakly $b(\Lambda,p)$-Open Functions, Int. J. Math. Comput. Sci. 19 (2024), 497–501.
[14] J. Khampakdee, C. Boonpok, Properties of $(\Lambda,p)$-Closed Functions, Int. J. Math. Comput. Sci. 19 (2024), 481–484.
[15] C. Klanarong, C. Boonpok, Characterizations of Weakly $\delta(\Lambda,p)$-Closed Functions, Int. J. Math. Comput. Sci. 19 (2024), 503–507.
[16] C. Klanarong, C. Boonpok, Characterizations of Weakly $s(\Lambda,p)$-Open Functions and Weakly $s(\Lambda,p)$-Closed Functions, Int. J. Math. Comput. Sci. 19 (2024), 809–814.
[17] A.S. Mashhour, I.A. Hasanein, S.N. El-Deeb, $\alpha$-Continuous and $\alpha$-Open Mappings, Acta Math. Hungar. 41 (1983), 213–218.
[18] A.S. Mashhour, M.E. Abd El-Monsef, S.N. El-Deeb, On Precontinuous and Weak Precontinuous Mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
[19] T. Noiri and V. Popa, A unified theory of closed functions, Bull. Math. Soc. Math. Roum. 49 (2006), 371–382.
[20] T. Noiri, On $\theta$-Precontinuous Functions, Int. J. Math. Math. Sci. 28 (2001), 285–292. https://doi.org/10.1155/s0161171201006500.
[21] T. Noiri, A Generalization of Closed Mappings, Atti Acad. Naz. Lincei Rend. Cl. Sci. Fiz. Mat. Nat. 54 (1973), 412–415. https://eudml.org/doc/293867.
[22] M.C. Pal, P. Bhattacharyya, Feeble and Strong Forms of Preirresolute Functions, Bull. Malays. Math. Soc. 19 (1996), 63–75.
[23] D.A. Rose, D.S. Jankovi\'{c}, Weakly Closed Functions and Hausdorff Spaces, Math. Nachr. 130 (1987), 105–110.
[24] D.A. Rose, On Weak Openness and Almost Openness, Int. J. Math. Math. Sci. 7 (1984), 35–40.
[25] N. Srisarakham, C. Boonpok, On Weakly $\delta(\Lambda,p)$-Open Functions, Int. J. Math. Comput. Sci. 19 (2024), 485–489.
[26] N. Viriyapong, S. Sompong, C. Boonpok, $(\tau_1,\tau_2)$-Extremal Disconnectedness in Bitopological Spaces, Int. J. Math. Comput. Sci. 19 (2024), 855–860.
[27] C. Viriyapong, C. Boonpok, $(\tau_1,\tau_2)\alpha$-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.