Best proximity point results for mixed multivalued mappings with
application to homotopy theory
Abstract
In this paper, first, we introduce a concept of mixed multivalued
contraction mapping. Then, we present some best proximity point results
for such mappings on 0-complete partial metric spaces. Hence, we extend
and generalize some famous and nice results existing in the literature
such as Abkar and Gabeleh, Gabeleh and Aydi et al. Also, we provide some
nontrivial illustrative examples to support our results and to compare
with the results mentioned before. Finally, the first time, we give some
applications to homotopy theory via new best proximity point results.
Hence, we obtain some best proximity point results for homotopic
mappings