Abstract
In this paper, using the concept of a w-distance on a metric space, we first prove the existence of a fixed point theorem for generalized w(alpha)-contraction multivalued mappings without completeness in metric spaces. Our presented results generalize, extend, and improve the result of Kutbi and Sintunavarat (Abstr. Appl. Anal. 2013:165434, 2013) and various well-known results on the topic in the literature. Also, we give some examples to which the results of Kutbi and Sintunavarat (Abstr. Appl. Anal. 2013:165434, 2013) are not applied, but our results are.