Document Type: Research Paper

Authors

1 Department of Mathematics, Mathematics Section, FEAT, Annamalai University, Annamalai Nagar, Tamil Nadu-608 002, India

2 Department of Mathematics, Mathematics Section, FEAT, Annamalai University, Annamalai Nagar, Tamil Nadu-608 002, India

Abstract

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

Keywords

Main Subjects

[1] K. K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82 (1) (1981), 14-32.

[2] A. Bhattacharyya, M. N. Mukherjee, On fuzzy δ-almost continuous and δ$^*$-almost continuous functions, J. Tripura Math. Soc. 2 (2000), 45-57.

[3] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.

[4] N. R. Das, P. C. Baishya, Mixed fuzzy topological space, The Journal of Fuzzy Math. 3 (4) (1995), pp.

[5] N. R. Das, P. C. Baishya, Study of some aspects of Mixed δ-pre fuzzy topological spaces, The Journal of Fuzzy Math. 20 (3) (2012), 613-626.

[6] E. Ekici, On fuzzy upper and lower s-limit sets, Chaos. Solitons and Fractals. 28 (2006), 1090-1098.

[7] E. Ekici, Some generalizations of almost contra-super-continuity, Filomat. 21 (2) (2007), 31-44.

[8] E. Ekici, On e-open sets, DP$^*$-sets and and DPϵ$^*$-setsand decompositions of continuity, Arab. J. Sci. Eng. 33 (2A) (2008), 269-282.

[9] E. Ekici, New forms of contra-continuity, Carpathian J. of Math. 24 (1) (2008), 37-45.

[10] E. Ekici, On a-open sets A$^*$-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Dudapest. Eotvos Sect. Math. 51 (2008), 39-51.

[11] E. Ekici, On e$^*$-open sets and (D,S)$^*$-sets, Mathematica Moravica. 13 (1) (2009), 29-36.

[12] M. E. El-Shafei, A. I. Aggour, Some weaker forms of fuzzy topologies on fuzzy function spaces, J. Egypt. Math. Soc. 16 (1) (2008), 27-35.

[13] S. Ganguly, S. Saha, A note on δ-continuity and δ-connected sets in fuzzy set theory, Simon Stevin. 62 (2) (1988), 127-141.

[14] J. C. Kelly, Bitopological spaces, Proc. London. Math. Soc. 13 (49) (1963), 71-89.

[15] S. R. Malghan, S. S. Benchalli, On open maps, closed maps and local compactness in fuzzy topological spaces, J. Math. Anal. Appl. 99 (2) (1984), 338-349.

[16] M. N. Mukherjee, S. P. Sinha, On some near-fuzzy continuous functions between fuzzy topological spaces, Fuzzy Sets and systems. 34 (1990), 245-254.

[17] A. Mukherjee, S. Debnath, delta$-semi-open sets in fuzzy setting, J. Tri. Math. Soc. 8 (2006), 51-54.

[18] P. M. Pu, Y. M. Liu, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith Convergence$^*$, J. Math. Anal. 76 (1980), 571-599.

[19] P. M. Pu, Y. M. Liu, Fuzzy topology II, Product and Quotient spaces, J. Math. Anal. Appl. 77 (1980), 20-37.

[20] V. Seenivasan, K. Kamala, Fuzzy e-continuity and fuzzy e-open sets, Ann. Fuzzy Math. Inform. 8 (1) (2014), 141-148.

[21] V. Seenivasan, K. Kamala, Some aspects of fuzzy e~-closed set, Ann. Fuzzy Math. Inform. 9 (6) (2015), 1019-1027.

[22] A. Vadivel, M. Palanisamy, Fuzzy completely weakly e-irresolute functions, Int. J. Sci. and Eng. Res. 6 (3) (2015), 128-135.

[23] A. Vadivel, B. Vijayalakshmi, Mixed e-fuzzy topological spaces, Int. J. Pure. Appl. Math. 113 (12) (2017), 115-122.

[24] A. Vadivel, B. Vijayalakshmi, On fuzzy generalized e-closed sets and maps in fuzzy topological spaces, Accepted.

[25] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353.