Some Common Fixed Point Theorems in Fuzzy Mappings
English
Jagdish C. Chaudhary, Jatin S. Patel, Shailesh T. Patel, Chirag R. Patel
2015
International Journal of Mathematics Trends and Technology
In this paper we established some fixed point and common fixed point theorem for sequence of fuzzy mappings and also taking rational inequalities which generalized the result of Heilpern [2], Lee, Cho, Lee and Kim [16] . Introduction: The concept of fuzzy sets was introduced by Zadeh [1] in 1965 . After that a lot of work has been done regarding fuzzy sets and fuzzy mappings. The concept of fuzzy mapping was first introduced by Heilpern[2], he proved fixed point theorem for fuzzy contraction
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... pings which is a fuzzy analogue of the fixed point theorem for multy valued mappings of Nadler[3], vijayraju and Marudai[4], generalized the Bose and Mukherjee's[5] fixed point theorems for contractive types fuzzy mappings. Marudai and srinmivasan [6] derived the simple proof of Heilpern's [2] theorem and generalization of Nadler's [3] theorem for fuzzy mappings. Bose and sahani [7], Butnariu [8-10], Chang and Huang , Non-jing [11], Chang [12], chitra [13], som and Mukharjee [14] , studied fixed point theorems for fuzzy mappings. Bose and Sahani [7], extends Heilpern's result for a pair of generalized fuzzy contraction mappings. Lee and cho [15], described a fixed point theorem for contractive type fuzzy mappings which is generalization of Heilpern's [2], result. Lee, cho, lee and kim [16] obtained a common fixed point theorem for a sequence of fuzzy mappings satisfying certain conditions, which is generalization of the second theorem of Bose and Sahini [7]. Recently Rajendra and Bala Subramanian [21], worked on fuzzy contraction mappings. More recently Vijayraju and Mohanraj [17], obtained some fixed point theorems for contractive type fuzzy mappings which are generalization of Beg and Azam [18], fuzzy extension of kirk and Downning [19], and which obtained simple proof of park and jeong [20] . In this paper we are proving some fixed point theorems in fuzzy mapping containing the rational expressions. Perhaps this is first time when we are including such types of rational expressions. These results are extended form of Heilpern [2], Lee, Cho, Lee and Kim [16] . Common fixed point theorems in fuzzy metric spaces for weakly compatible mappings along with property (E.A.) satisfying implicit relation by Asha Rani [22] .
doi:10.14445/22315373/ijmtt-v20p512
fatcat:674zfhaybvckjnnu5bphvcer3q