Strong Forms of Mixed Continuity

P.Thangavelu; S.Premakumari

doi:https://doi.org/10.14445/22315373/IJMTT-V61P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 61 | Number 1 | Year 2018 | Article Id. IJMTT-V61P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P506

Strong Forms of Mixed Continuity

P.Thangavelu, S.Premakumari

Abstract

Multivalued functions between topological spaces have applications to the fixed point theory which in turn has applications to social science, science and engineering. The authors have recently studied upper mixed continuous, lower mixed continuous multifunctions and their weak forms between topological spaces. The purpose of this paper is to introduce and characterize some strong forms of upper and lower mixed continuous multifunctions.

Keywords

Multifunctions, mixed continuity, almost continuity, clopen continuity.

References

[1] Abd El-Monsef M.E., Nasef A.A, On Multifunctions, Chaos Solitons Fractals, 12(2001), 2387-2394.
[2] M.Agdag, Weak and strong forms of continuity of multifunctions, Chaos Solitions and Fractals 32(2007)1337-1344.
[3] M.Agdag, On super continuous multifunctions, Acta Math.Hungar. 99(1-2)(2003), 143-153.
[4] C.D.Aliprants and K.C.Border, Infinite Dimensional Analysis-A Hitchhiker’s guide,2nd edition, Springer-verlag, 1999.
[5] J.P.Aubin and H.Frankowska, Set valued analysis, Birkhauser, Basel, 1990.
[6] G.Beer, Topologies on closed sets and closed convex sets, Kluwer Academic Publishers, 1993.
[7] Carlos J.R. Borges, A study of multivalued functions, Pacific J. of Math. 23(3)(1967) 451-461.
[8] J.Ceo and I.J.Reilly, On -continuous multifunctions and paralindelofness, Indian j.Pure Appl.Math. 26(11)(1995), 1099-1110.
[9] Eubica Hola and Branislav Novotny, Sub continuity, Math.Slovaca 62(2)(2012) 345-362.
[10] W.W.Hogan, Point-to-set maps in mathematical programming, SIAM Review 15(3)(1973) 591-603.
[11] S.Hu, N.S. Papageorgiou, Handbook of multivalued analysis Vol.1, Kluwer Academic Publishers, 1997.
[12] Kanbir A and Reilly I.L, On some variations of multifunction continuity, Applied General topology, 9(2)92008), 301-310.
[13] Marian Przemski, Decompositions of continuity for multifunctions, Hacettepe journal of Mathematics and Statistics, 46(4)(2017), 621-628.
[14] E.A.Michael, Continuous Selections I, Ann.of Math. 63(1956) 361-382.
[15] E.A.Michael, Continuous Selections II, Ann.of Math. 64(1956) 562-580.
[16] T.Noiri and V.Popa, Weakly quasi continuous multifunctions, Ancl.Univ.Timisoara, Ser.Mat. 26(1988).
[17] V.I.Ponomarev, A new space of closed sets and multivalued continuous mappings of bicompacta, Amer.Math. Soc. Transl. 38(2)(1964) 95-118.
[18] V.I.Ponomarev, Properties of topological spaces preserved under multivalued continuous mappings, Amer.Math. Soc. Transl. 38(2)(1964) 119-140.
[19] V.I.Ponomarev, On the extensions of multivalued mappings of topological spaces to their compactifications, Amer.Math.Soc.Transl. 38(2)(1964) 141-158.
[20] M.Przemski, Some generalization of continuity and quasi continuity of multivalued maps, Demonstratio Math.26(1993), 381-400.
[21] S.M.Robinson, Some continuity properties of polyhedral multifunctions, Math.Prog.Study 14(1991) 206-214.
[22] S.M.Robinson, Regularity and stability for convex multivalued functions, Math.of OR 1(1976)130-143.
[23] R.E..Smithson, Some general properties of multivalued functions, Pacific J. Math. 15(1965) 681-703.
[24] Smithson R E, Almost and weak continuity for multifunctions, Bull. Calcutta Math. Soc., 70(1978), 383-390.
[25] M.Stone, Applications of the theory of boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 374-481.
[26] W.Strother, Continuous multivalued functions, Boletin da Sociedade de S.Paulo 10(1958) 87-120.
[27] W.Strother, On an open question concerning fixed points, Proc.Amer.Math Soc. 4(1953) 988-993.
[28] P.Thangavelu and S.Premakumari, Mixed Continuity, International Conference on Applied and Computational Mathematics, 10 August 2018, Erode Arts and Science College, Erode-638009, Tamil Nadu, India.
[29] P.Thangavelu and S.Premakumari, Weak forms of mixed continuity, International Journal of Advanced Research in Science, Engineering and Technology (Accepted).
[30] Valeriu Popa, A note on weakly and almost continuous multifunctions, Univ.Novom Sadhu, Zb Rad.Prirod.Mat.Fac.Ser.Mat.21(1991), 31-38.
[31] Valeriu Popa and Takashi Noiri, On some weak forms of continuity for multifunctions, Istanbul Univ.Fen.Mat. Der.60(2001), 55-72.
[32] Valeriu Popa and Takashi Noiri, On upper and lower almost quasi continuous multifunctions, Bull.Inst.Math.Acad.Sinica 21(1993), 337-349.
[33] V.Popa, Multifunctions semicontinuous , Rev.Roumaine Math.Pures Appl. 27(1982), 807-815.
[34] V.Popa and T.Noiri, On some weak forms of continuity for multifunctions, Istanbul Univ.Fen.Fak.Mat.Der.60(2001), 55-72.
[35] N.V.Velicko, H-closed topological spaces, Amer. Math. Soc. Trans. 78 (1968), 103-118,

Citation :

P.Thangavelu, S.Premakumari, "Strong Forms of Mixed Continuity," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 1, pp. 43-50, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P506