Some Results on Fuzzy Mappings for Rational Expressions

The concept of fuzzy sets was introduced by Zadeh [21] in 1965. After that a lot of work has been done regarding fuzzy sets and fuzzy mappings. The concept of fuzzy mappings was first introduced by Heilpern [10], he proved fixed point theorem for fuzzy contraction mappings which is a fuzzy analogue of the fixed point theorem for multi valued mappings of Nadler [15], Vijayraju and Marudai [19] generalized the Bose and Mukherjee , s[2] fixed point theorems for contractive types fuzzy mappings .Marudai and Srinmivasan [14] derived the simple proof of Heilpern , s [10] theorem and generalization of Nadler ’ s [15] theorem for fuzzy mappings. Bose and Sahani [3], Butnariu [4,5,6], Chang and Huang [7], Chang [8], Chitra [9], Som and Mukharjee [18] studied fixed point theorems for fuzzy mappings. Bose and Sahini[3] extends Heilpern , s result for a pair of generalized fuzzy contraction mappings .Lee and Cho[13] described a fixed point theorem for contractive type fuzzy mappings which is generalization of Heilpern , s [10] result. Lee, Cho, Lee and Kim [13] 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 [3]. Recently, Rajendran and Balasubramanian [17] worked on fuzzy contraction mappings. More recently Vijayraju and Mohanraj [20] obtained some fixed point theorems for contractive type fuzzy mappings which are generalization of Beg and Azam [1], fuzzy extension of Kirk and Downing [11] and which obtained by the simple proof of Park and Jeong [16] . In the present paper we are proving some fixed point and common fixed point theorems in fuzzy mappings containing the rational expressions.