Abstract

In this paper, first we give a theorem which generalizes the Banach contraction principle and fixed point theorems given by many authors, and then a fixed point theorem for a multi-valued $(\theta, L)$-weak contraction. We extend the notion of $(\theta,L)$-weak contraction to fuzzy mappings and obtain some fixed point theorems. A coincidence point theorem for a hybrid pair of mappings $f:X\to X$ and $T:X\to W(X)$ is established. Later on we prove a fixed point theorem for a different type of fuzzy mapping.

Keywords: Contraction mapping; fixed point; Banach contraction principle; Hausdorff metric; fuzzy set; fuzzy mapping.

MSC: 03E72, 47H10, 54H25

Pages:  7$-$26     

Volume  63 ,  Issue  1 ,  2011