Abstract
In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of
Olgun, Minak and Altun
[M. Olgun, G. Minak and I. Altun,
A new approach to Mizoguchi–Takahashi type fixed point theorems,
J. Nonlinear Convex Anal. 17 2016, 3, 579–587], we improve these theorems with a new generalization contraction condition for multivalued mappings in incomplete metric spaces. This result is a significant generalization of some well-known results in the literature. Also, we provide some examples to show that our main theorems are a generalization of previous results. Finally, we give an application to a boundary value differential equation.