Fixed point, data dependence and well-posed problems on $$\mathcal {H}^+$$ H + -metric spaces and their application to homotopy theory

Abstract

In this paper, we propose some fixed point results for a new type of contractive multivalued operators in the setting of \(\mathcal {H}^+\)-metric spaces which are further applied to get results on data dependence and well-posed multivalued problems. By doing this, our work generalizes Nadler’s, Kikkawa and Suzuki’s, and some other fixed point theorems. The theorems provided allow upgrading of Pathak and Shahzad’s and Popescu’s results which is shown by an example. A homotopy result is presented at the end as an application of our main theorem.