In the present paper, we give a generalization of Mizoguchi-Takahashi's fixed point theorem, which is a partial solution of Reich's original problem concerning multivalued mappings on complete metric spaces.

In this paper, we present some fixed point results for multivalued mappings with both closed values and proximinal values on left K-complete quasi metric spaces. We also provide a nontrivial example to illustrate our results.

Let (X, d) be a metric space, A and B be two nonempty subsets of X, and T : A. B be a mapping. In this case, since the equation x = Tx may not have an exact solution, it is meaningful to explore the approximate solution. ...

In the light of the paper of Hasanzade Asl et al. (Fixed Point Theory Appl. 2012: 212, 2012, doi:10.1186/1687-1812-2012-212), we obtain a fixed point theorem for multivalued mappings on a complete metric space. Our result ...

In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the well-known Mizoguchi-Takahashi fixed point theorem, which is the closest answer to Reich's conjecture about the existence ...

In the present paper, considering the Jleli and Samet's technique we give many fixed point results for multivalued mappings on complete metric spaces without using the Pompeiu-Hausdorff metric. Our results are real ...