Upper and lower $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions

Subject Areas : Functional analysis

M. Akdag ¹ , F. Erol ²

1 - Cumhuriyet University Science Faculty Department of Mathematics 58140 S_IVAS / TURKEY
2 - Cumhuriyet University Science Faculty Department of Mathematics 58140 S_IVAS / TURKEY

Received: 2014-06-12 Accepted : 2015-03-15 Published : 2015-04-01

Keywords: Generalized open sets, multifunction, generalized continuity,

Abstract :

In this paper, a new class of multifunctions, called generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions, has been defined and studied. Some characterizations and severalproperties concerning generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions are obtained. The relationships between generalized $\alpha(\mu_{X},\mu_{Y})$-continuous multifunctions and some known concepts are also discussed.

References:

[1] A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar., 96, 351-357, 2002.

[2] A. Csaszar, Extremally disconnected generalized topologies, Annales Univ. Sci. Budapest., 47, 91-96, 2004.

[3] A. Csaszar, ”δ−and θ−modifications of generalized topologies,” Acta Mathematica Hungarica, vol. 120, pp. 274-279, 2008.

[4] A. Csaszar, ”Product of generalized topologies,” Acta Mathematica Hungarica, vol. 123, no:1-2, pp. 127-132, 2009.

[5] A. Csaszar, γ-connected sets, Acta Math. Hungar., 101, 273-279, 2003.

[6] A. Csaszar, ”Further remarks on the formula for γ−interior,” Acta Mathematica Hungarica, vol. 113, no: 4, pp. 325-332, 2006.

[7] A. Csaszar, ”Generalized open sets in generalized topologies,” Acta Mathematica Hungarica, vol. 106,no: 1-2 pp. 53-66, 2005.

[8] A. Kanibir and I. L. Reilly, ”Generalized continuity for multifunctions, ” Acta Mathematica Hungarica, vol. 122, no . 3, pp. 283-292, 2009.

[9] A. S. Mashour, M. E. Abd El-Monsef, and S. N. El-Deeb, ”On precontinuous and weakprecontinuous functions, ”Proceedings of the Mathematical and Physical Society of Egypt, pp. 47-53, 1982.

[10] C. Berge, Topological Spaces, Macmillian, New York, 1963. English translation by E. M. Patterson of Espaces Topologiques, Fonctions Multivoques, Dunod, Paris, 1959.

[11] C. Cao, J. Yang, W. Wang, B. Wang, Some generalized continuities functions on generalized topological spaces, Hacettepe Jou. of Math. and Stat., 42(2), 159-163, 2013.

[12] C. Boonpok, ”On upper and Lower β (µX, µY )- Continuous multifunctions”, Int. J. of Math. and Math. Sci., 2012 Doi: 10. 1155/2012/931656.

[13] D. Andrijevic, ”Semipreopen sets, ” Matematicki Vesnik, vol. 38, no. 2, pp. 24-32, 1986.

[14] J. P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, 1990.

[15] M. Akdag and F. Erol, Upper and Lower P re(µX, µY ) Continuous Multifunctions, Scientific Journal of Mathematics Research Oct. 2014, Vol. 4 Iss. 5, PP. 46-52.

[16] M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, ”β-open sets and β-continuous mapping, ”Bulletin of the Faculty of Science. Assiult Universty, vol. 12, no. 1, pp. 77-90, 1983.

[17] N. Levine, ”Semi-open sets and semi-contiuity in topological spaces, ” The American Mathematical Montly, vol. 70, pp. 36-41, 1963.

[18] O. Njastad, On some classes of nearly open sets, Pacific Journal of Math., vol.15, 961-870, 1965.

[19] R. Shen, Remarks on products of generalized topologies, Acta Math. Hungar., 124, 363-369, 2009.

[20] R. Shen, A note on generalized connectedness, Acta Math. Hungar., 122, 231-235, 2009.

[21] W. K. Min, Generalized continuous functions defined by generalized open sets on generalized topological spaces, Acta Math. Hun., 128, 299-306, 2010.