Abstract—In the present paper, first we introduce the notion of subsequential continuous mappings in the framework of fuzzy metric space and show that this concept is more general than continuous mappings as well as reciprocal continuous mappings. Also, we cited an example in support of this. Secondly, we introduce the concept of occasionally weakly compatible mappings which is more general than weakly compatible mappings in fixed point theory. At the end, we prove an interesting common fixed point theorem in fuzzy metric space for four self mappings by employing the notion of subsequential continuity, occasionally weakly compatible mappings and semi-compatible mappings.

Index Terms—Common fixed point, compatible maps, continuous t-norm, fuzzy metric space, subsequential continuity, semi-compatible maps and occasionally weakly compatible maps.

Arihant Jain is with the Department of Applied Mathematics, Shri Guru Sandipani Institute of Technology and Science, Ujjain (M.P.) 456 550 India (email: arihant2412@gmail.com).
V. H. Badshah is with School of Studies in Mathematics, Vikram University, Ujjain (M.P.) India.
V. K. Gupta is with the Department of Mathematics, Govt. Madhav Science College, Ujjain (M.P.) 456010 India.
Arvind Kumar Sharma is with the Department of Applied Mathematics, MITM, Ujjain (M.P.) India.

Cite: Arihant Jain, V. H. Badshah, V. K. Gupta, and Arvind Kumar Sharma, "Fixed Points for Subsequential Continuous Mappings in Fuzzy Metric Space," International Journal of Applied Physics and Mathematics vol. 4, no. 5, pp. 324-331, 2014.