We prove some coincidence and fixed point theorems for generalized ( ϕ , f ) -contractive type and f -nonexpansive type multivalued and singlevalued mappings in metric and Banach spaces, respectively. Our results extend, improve, and unify a few known results due to Browder, Browder and Petryshyn, Chang, Huang, and Cho, Husain and Latif, Husain and Tarafdar, and Karlovitz.