Fixed point theorems for some generalized contractive multi-valued mappings and fuzzy mappings

Abstract

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