A convexity of functions on convex metric spaces of Takahashi and applications
Ahmed A. Abdelhakim

TL;DR
This paper explores a new form of convexity called $W$-convexity for functions on convex metric spaces, generalizing classical convex functions and applying these concepts to fixed point theory and metric projection problems.
Contribution
It introduces the concept of $W$-convexity, extending convex functions to metric spaces, and demonstrates their properties and applications in convex analysis and fixed point theory.
Findings
$W$-convex functions generalize classical convex functions
Properties of $W$-convex functions align with convex analysis
Applications to metric projection and fixed point problems
Abstract
We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions on these spaces and refer to it as convexity. convex functions generalize convex functions on linear spaces. We discuss illustrative examples of (strict) convex functions and dedicate the major part of this paper to proving a variety of properties that make them fit in very well with the classical theory of convex analysis. Finally, we apply some of our results to the metric projection problem and fixed point theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
