Fuzzy mappings and fixed point theorem

Fuzzy fixed point theorems for multivalued fuzzy contractions in b -metric spaces

“…In 1981, Heilpern [20] obtained a fixed point theorem for fuzzy contraction mappings, which is a generalization of the fixed point theorem for multivalued mappings of Nadler's contraction principle. Subsequently, several authors generalized and studied the existence of fixed points and common fixed points of fuzzy mappings satisfying a contractive type condition (see [1,2,5,6,13,18,19,21,23,26,27,28,29,32]).…”

Fuzzy fixed point theorems for fuzzy mappings via β-admissible with applications

“…Afterward, many mathematicians [5][6][7][8][9] generalized the result given in [4]. Recently, Abbas and Turkoglu [10] established the existence of a fuzzy fixed point theorem for fuzzy mapping of a generalized contractive mapping on a complete metric space, which generalized and extended the results in [4] and many known results in [2,6].…”

“…Several researches were conducted on the generalizations of the concept of a fuzzy set. Heilpern [2] introduced the concept of fuzzy contraction mappings which maps from an arbitrary set to a certain subfamily of fuzzy sets in a metric linear space X. He also proved the existence of a fuzzy fixed point theorem which is a generalization of Nadler's [3] fixed point theorem for multivalued mappings.…”

Common fixed point theorems for a countable family of fuzzy mappings

“…Theorem 3.6 (Bose and Sahani 1]). Let (X; d) be a complete linear space and let F 1 and F 2 be fuzzy mappings from X to W(X) satisfying the following condition: For any x; y in X, D(F 1 (x); F 2 (y)) a 1 p(x; F 1 (x)) + a 2 p(y; F 2 (y)) + a 3 p(y; F 1 (x)) +a 4 p(x; F 2 (y)) + a 5 d(x; y) where a 1 , a 2 , a 3 , a 4 , a 5 , are non-negative real numbers, a 1 +a 2 +a 3 +a 4 +a 5 < 1 and a 1 = a 2 or a 3 = a 4 . Then there exists z 2 X such that fzg F i (z), i = 1; 2:…”