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Upper and Lower &delta;<sub>ij</sub>-Continuous Multifunctions

Year 2018, Issue: 21, 49 - 58, 27.02.2018

Abstract

In this paper we introduce and study the notions of upper and lower &delta;<sub>ij</sub>-continuous multifunctions. Several characterizations and properties concerning upper and lower &delta;<sub>ij</sub>-continuous multifunctions and other known forms of multifunctions introduced previously are investigated.

References

  • [1] M. E. Abd El-Monsef and A. A. Nasef, On multifunctions. Chaos, Solitions and Fractals, 12(2001), 2387-2394.
  • [2] C. Berge, Espacts topologiques, Fonctiones Hultivoques,Dunoud, Paris, 1959.
  • [3] J. Coa and I. L. Reilly, Nearly compact spaces and ±¤-continuous functions, Bollerttino UMI, (7)10-A(1996), 435-444.
  • [4] E. Ekici, Nearly continuous multifunctions. Acta Math. Univ. Comenianae 2(42) (2003), 229-235.
  • [5] M. S. El-Naschie, Topics in the mathematical physics of E-In¯nity theory, Chaos, Solitons and Fractals 30(3)(2006), 656-663.
  • [6] M. S. El-Naschine,, Quantum gravity, Cli®ord algebra, Fuzzy set theory and the fundamental constants of nature, Chaos, Solitons, Fractals 20(2004), 437-450.
  • [7] A. Kandil, E. E. Kerre, M. E. EL-Sha®ei and A. A. Nouh, Quasi µ-proximity spaces and pairwise µ-perfect irreducible. J. Austral Math. Soc., (Series A) 25 (1992), 322-333.
  • [8] J. C. Kelly, Bitopological spaces. Proc. London Math. Soc., 13(1963), 71-89.
  • [9] E. Klein and A. C. Thompson, Theory of correspondence, including applications to mathematical economic, John Wiley and Sons, 1984.
  • [10] Y. Kucuk, On some charecterizations of ±-continuous multifunctions. Demonstratio Mathematica 28 (1995)(3), 587-595.
  • [11] M. Kucuk and Y. Kucuk, Further properties of almost continuous multifunctions defined between bitopological spaces. Demonstratio Mathematica 29(3)(1995), 511-522.
  • [12] M. N. Mukherjee, G. K. Banerjee and S. Malakar, Bitopological QHC spaces.Indian J. Pure Appl. Math. 21(7)(1990), 639-648.
  • [13] M. N. Mukherjee and Ganguly, Generalization of almost continuous multifunctions to bitopological spaces. Bull. Cal. Math. Soc., 79(1987), 274-283.
  • [14] A. A. Nasef, Another weak forms of faint continuity, Chaos, Solitons and Fractals 12(2001),2219-2225.
  • [15] V. Popa, Multifunctions and bitopological spaces, Bull. Math. Soc. Sci. R. S. Romanic (N.S.) 67(19)(1976),147-152.
  • [16] V. Popa and T. Noiri, On upper and lower ®-precontinuous multifunctions Math. Slovaca 43(1996), 381-396.
  • [17] A. R. Singal and S. P. Arya, On pairwise almost regular spaces. Glasnik Math. 26(6)(1971), 335-343.
  • [18] R. E. Smithson, Maultifunctions and bitopological spaces. J. Nature. Sci. Math. 11(1972), 31-53.
Year 2018, Issue: 21, 49 - 58, 27.02.2018

Abstract

References

  • [1] M. E. Abd El-Monsef and A. A. Nasef, On multifunctions. Chaos, Solitions and Fractals, 12(2001), 2387-2394.
  • [2] C. Berge, Espacts topologiques, Fonctiones Hultivoques,Dunoud, Paris, 1959.
  • [3] J. Coa and I. L. Reilly, Nearly compact spaces and ±¤-continuous functions, Bollerttino UMI, (7)10-A(1996), 435-444.
  • [4] E. Ekici, Nearly continuous multifunctions. Acta Math. Univ. Comenianae 2(42) (2003), 229-235.
  • [5] M. S. El-Naschie, Topics in the mathematical physics of E-In¯nity theory, Chaos, Solitons and Fractals 30(3)(2006), 656-663.
  • [6] M. S. El-Naschine,, Quantum gravity, Cli®ord algebra, Fuzzy set theory and the fundamental constants of nature, Chaos, Solitons, Fractals 20(2004), 437-450.
  • [7] A. Kandil, E. E. Kerre, M. E. EL-Sha®ei and A. A. Nouh, Quasi µ-proximity spaces and pairwise µ-perfect irreducible. J. Austral Math. Soc., (Series A) 25 (1992), 322-333.
  • [8] J. C. Kelly, Bitopological spaces. Proc. London Math. Soc., 13(1963), 71-89.
  • [9] E. Klein and A. C. Thompson, Theory of correspondence, including applications to mathematical economic, John Wiley and Sons, 1984.
  • [10] Y. Kucuk, On some charecterizations of ±-continuous multifunctions. Demonstratio Mathematica 28 (1995)(3), 587-595.
  • [11] M. Kucuk and Y. Kucuk, Further properties of almost continuous multifunctions defined between bitopological spaces. Demonstratio Mathematica 29(3)(1995), 511-522.
  • [12] M. N. Mukherjee, G. K. Banerjee and S. Malakar, Bitopological QHC spaces.Indian J. Pure Appl. Math. 21(7)(1990), 639-648.
  • [13] M. N. Mukherjee and Ganguly, Generalization of almost continuous multifunctions to bitopological spaces. Bull. Cal. Math. Soc., 79(1987), 274-283.
  • [14] A. A. Nasef, Another weak forms of faint continuity, Chaos, Solitons and Fractals 12(2001),2219-2225.
  • [15] V. Popa, Multifunctions and bitopological spaces, Bull. Math. Soc. Sci. R. S. Romanic (N.S.) 67(19)(1976),147-152.
  • [16] V. Popa and T. Noiri, On upper and lower ®-precontinuous multifunctions Math. Slovaca 43(1996), 381-396.
  • [17] A. R. Singal and S. P. Arya, On pairwise almost regular spaces. Glasnik Math. 26(6)(1971), 335-343.
  • [18] R. E. Smithson, Maultifunctions and bitopological spaces. J. Nature. Sci. Math. 11(1972), 31-53.
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Arafa Nasef

Abd-el Ftah. Abd Alla. Azzam This is me

Nada Seyam This is me

Publication Date February 27, 2018
Submission Date December 24, 2017
Published in Issue Year 2018 Issue: 21

Cite

APA Nasef, A., Azzam, A.-e. F. A. A., & Seyam, N. (2018). Upper and Lower δij-Continuous Multifunctions. Journal of New Theory(21), 49-58.
AMA Nasef A, Azzam AeFAA, Seyam N. Upper and Lower δij-Continuous Multifunctions. JNT. February 2018;(21):49-58.
Chicago Nasef, Arafa, Abd-el Ftah. Abd Alla. Azzam, and Nada Seyam. “Upper and Lower δij-Continuous Multifunctions”. Journal of New Theory, no. 21 (February 2018): 49-58.
EndNote Nasef A, Azzam A-eFAA, Seyam N (February 1, 2018) Upper and Lower δij-Continuous Multifunctions. Journal of New Theory 21 49–58.
IEEE A. Nasef, A.-e. F. A. A. Azzam, and N. Seyam, “Upper and Lower δij-Continuous Multifunctions”, JNT, no. 21, pp. 49–58, February 2018.
ISNAD Nasef, Arafa et al. “Upper and Lower δij-Continuous Multifunctions”. Journal of New Theory 21 (February 2018), 49-58.
JAMA Nasef A, Azzam A-eFAA, Seyam N. Upper and Lower δij-Continuous Multifunctions. JNT. 2018;:49–58.
MLA Nasef, Arafa et al. “Upper and Lower δij-Continuous Multifunctions”. Journal of New Theory, no. 21, 2018, pp. 49-58.
Vancouver Nasef A, Azzam A-eFAA, Seyam N. Upper and Lower δij-Continuous Multifunctions. JNT. 2018(21):49-58.


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