Abstract
In this work, we give a graphical version of the Ekeland variational principle which enables us to discover a new version of the Caristi fixed point theorem in weighted digraphs not necessarily generated by a partial order. Then we show that both graphical versions of the Ekeland variational principle and Caristi's fixed point theorem are equivalent. In addition, we applied our main result on a differential structure Banach space.
| Original language | English |
|---|---|
| Pages (from-to) | 5313-5321 |
| Number of pages | 9 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 147 |
| Issue number | 12 |
| DOIs | |
| State | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2019 American Mathematical Society.
Keywords
- Brønsted partial order
- Caristi
- Ekeland variational principle
- Fixed point
- Weighted graph
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics