Almost Near \(\tau^\star(\sigma_1,\sigma_2)\)-Continuity for Multifunctions

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Jeeranunt Khampakdee, Areeyuth Sama-Ae, Chawalit Boonpok

Abstract

This paper presents a new concept of continuous multifunctions defined between an ideal topological space and a bitopological space, called almost nearly \(\tau^\star(\sigma_1,\sigma_2)\)-continuous multifunctions. Moreover, several characterizations and some properties concerning almost nearly \(\tau^\star(\sigma_1,\sigma_2)\)-continuous multifunctions are established.

Article Details

References

  1. C. Boonpok, N. Srisarakham, $(tau_1,tau_2)$-Continuity for Functions, Asia Pac. J. Math. 11 (2024), 21. https://doi.org/10.28924/APJM/11-21.
  2. C. Boonpok, P. Pue-On, Characterizations of Almost $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 22 (2024), 33. https://doi.org/10.28924/2291-8639-22-2024-33.
  3. C. Boonpok, C. Klanarong, On Weakly $(tau_1,tau_2)$-Continuous Functions, Eur. J. Pure Appl. Math. 17 (2024), 416–425. https://doi.org/10.29020/nybg.ejpam.v17i1.4976.
  4. C. Boonpok, $(tau_1,tau_2)delta$-Semicontinuous Multifunctions, Heliyon, 6 (2020), e05367. https://doi.org/10.1016/j.heliyon.2020.e05367.
  5. 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.
  6. C. Carpintero, J. Pacheco, N. Rajesh, E. Rosas, S. Saranyasri, Properties of Nearly $omega$-Continuous Multifunctions, Acta Univ. Sapientiae, Math. 9 (2017), 13–25. https://doi.org/10.1515/ausm-2017-0002.
  7. M. Chiangpradit, S. Sompong, C. Boonpok, Weakly Quasi $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 22 (2024), 125. https://doi.org/10.28924/2291-8639-22-2024-125.
  8. N. Chutiman, S. Sompong, C. Boonpok, Characterizations of Nearly $(tau_1,tau_2)$-Continuous Functions, Asia Pac. J. Math. 12 (2025), 27. https://doi.org/10.28924/APJM/12-27.
  9. N. Chutiman, A. Sama-Ae, C. Boonpok, Almost Near $(tau_1,tau_2)$-Continuity for Multifunctions, Eur. J. Pure Appl. Math. 18 (2025), 5650. https://doi.org/10.29020/nybg.ejpam.v18i1.5650.
  10. E. Ekici, Almost Nearly Continuous Multifunctions, Acta Math. Univ. Comen. New Ser. 73 (2004), 175–186. https://eudml.org/doc/126719.
  11. E. Ekici, Nearly Continuous Multifunctions, Acta Math. Comenianae, 72 (2003), 229–235.
  12. D. Jankovic, T.R. Hamlet, New Topologies from Old via Ideals, Am. Math. Mon. 97 (1990), 295–310. https://doi.org/10.2307/2324512.
  13. J. Khampakdee, A. Sama-Ae, C. Boonpok, Upper and Lower Continuous Multifunctions Defined Between an Ideal Topological Space and a Bitopological Space, Eur. J. Pure Appl. Math. 18 (2025), 6565. https://doi.org/10.29020/nybg.ejpam.v18i3.6565.
  14. C. Klanarong, S. Sompong, C. Boonpok, Upper and Lower Almost $(tau_1,tau_2)$-Continuous Multifunctions, Eur. J. Pure Appl. Math. 17 (2024), 1244–1253. https://doi.org/10.29020/nybg.ejpam.v17i2.5192.
  15. B. Kong-ied, A. Sama-Ae and C. Boonpok, Almost Nearly $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 23 (2025), 14. https://doi.org/10.28924/2291-8639-23-2025-14.
  16. B. Kong-ied, A. Sama-Ae, C. Boonpok, Almost Quasi $tau^star(sigma_1,sigma_2)$-Continuous and Weakly Quasi $tau^star(sigma_1,sigma_2)$-Continuous Functions, Eur. J. Pure Appl. Math. 18 (2025), 6572. https://doi.org/10.29020/nybg.ejpam.v18i3.6572.
  17. B. Kong-ied, S. Sompong, C. Boonpok, Almost Quasi $(tau_1,tau_2)$-Continuous Functions, Asia Pac. J. Math. 11 (2024), 64. https://doi.org/10.28924/APJM/11-64.
  18. K. Kuratowski, Topology, Academic Press, 1966.
  19. S.N. Maheshwari, G.I. Chae, P.C. Jain, Almost Feebly Continuous Functions, Ulsan Inst. Tech. Rep. 13 (1982), 195–197.
  20. S.R. Malghan, V.V. Hanchinamani, $mathrm{N}$-Continuous Functions, Ann. Soc. Sci. Bruxelles, 98 (1984), 69–79.
  21. S. Marcus, Sur les Fonctions Quasicontinues au Sense de S. Kempisty, Colloq. Math. 8 (1961), 47–53. http://eudml.org/doc/210887.
  22. B.M. Munshi, D.S. Bassan, Almost Semi-Continuous Mappings, Math. Student, 49 (1981), 239–248.
  23. T. Noiri, V. Popa, On $(mI,nJ)$-Continuous Multifunctions, Rom. J. Math. Comput. Sci. 15 (2025), 1–8.
  24. T. Noiri, V. Popa, A Unified Theory of Upper and Lower Almost Nearly Continuous Multifunctions, Math. Balkanica, 23 (2009), 51–72.
  25. T. Noiri, N. Ergun, Notes on $mathrm{N}$-Continuous Functions, Res. Rep. Yatsushiro Coll. Tech. 11 (1989), 65–68.
  26. V. Popa, Almost Continuous Multifunctions, Mat. Vesnik, 6 (1982), 75–84.
  27. V. Popa, on a Decomposition of Quasicontinuity in Topological Spaces, Stud. Cerc. Mat. 30 (1978), 31–35.
  28. P. Pue-on, A. Sama-Ae, C. Boonpok, Characterizations of Nearly $tau^star(sigma_1,sigma_2)$-Continuous Functions, (Submitted).
  29. P. Pue-on, A. Sama-Ae, C. Boonpok, On Weak Forms of Upper and Lower Continuous Multifunctions Between an Ideal Topological Space and a Bitopological Space, Eur. J. Pure Appl. Math. 18 (2025), 6567. https://doi.org/10.29020/nybg.ejpam.v18i3.6567.
  30. P. Pue-on, S. Sompong, C. Boonpok, Weakly Quasi $(tau_1,tau_2)$-Continuous Multifunctions, Eur. J. Pure Appl. Math. 17 (2024), 1553–1564. https://doi.org/10.29020/nybg.ejpam.v17i3.5191.
  31. P. Pue-on, S. Sompong, C. Boonpok, Almost Quasi $(tau_1,tau_2)$-Continuity for Multifunctions, Int. J. Anal. Appl. 22 (2024), 97. https://doi.org/10.28924/2291-8639-22-2024-97.
  32. P. Pue-on, S. Sompong, C. Boonpok, Upper and Lower $(tau_1,tau_2)$-Continuous Mulfunctions, Int. J. Math. Comput. Sci. 19 (2024), 1305–1310.
  33. M.K. Singal, A.R. Singal, Almost Continuous Mappings, Yokohama J. Math. 16 (1968), 63–73.
  34. M. Thongmoon, A. Sama-Ae, C. Boonpok, Almost Quasi Continuity and Weak Quasi Continuity for Multifunctions Between an Ideal Topological Space and a Bitopological Space, Eur. J. Pure Appl. Math. 18 (2025), 6571. https://doi.org/10.29020/nybg.ejpam.v18i3.6571.
  35. M. Thongmoon, A. Sama-Ae, C. Boonpok, Upper and Lower Near $(tau_1,tau_2)$-Continuity, Eur. J. Pure Appl. Math. 18 (2025), 5633. https://doi.org/10.29020/nybg.ejpam.v18i1.5633.
  36. M. Thongmoon, S. Sompong, C. Boonpok, Upper and Lower Weak $(tau_1,tau_2)$-Continuity, Eur. J. Pure Appl. Math. 17 (2024), 1705–1716. https://doi.org/10.29020/nybg.ejpam.v17i3.5238.
  37. N. Viriyapong, A. Sama-Ae, C. Boonpok, On Almost $tau^star(sigma_1,sigma_2)$-Continuity and Weak $tau^star(sigma_1,sigma_2)$-Continuity, Eur. J. Pure Appl. Math. 18 (2025), 6568. https://doi.org/10.29020/nybg.ejpam.v18i3.6568.
  38. C. Viriyapong, A. Sama-Ae, C. Boonpok, Almost Continuity for Multifunctions Defined from an Ideal Topological Space into a Bitopological Space, Eur. J. Pure Appl. Math. 18 (2025), 6566. https://doi.org/10.29020/nybg.ejpam.v18i3.6566.
  39. N. Viriyapong, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Extremal Disconnectedness in Bitopological Spaces, Int. J. Math. Comput. Sci. 19 (2024), 855–860.
  40. C. Viriyapong, C. Boonpok, $(tau_1,tau_2)alpha$-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.