Sadovskiiʹs fixed point theorem without convexity Original Research Article

The abstract formulation of Kirkʹs fixed point theorem by Penot played a major role in developing fixed point theorems in nonconvex setting. In this work, we similarly give an abstract formulation to Sadovskiiʹs fixed point theorem using convexity structures. As an example, we discuss these new ideas in the hyperconvex metric setting.