@article{5d50fa94de894e369e76067e43ea09b6,
title = "Ekeland variational principle on weighted graphs",
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.",
keywords = "Br{\o}nsted partial order, Caristi, Ekeland variational principle, Fixed point, Weighted graph",
author = "Alfuraidan, {Monther Rashed} and Khamsi, {Mohamed Amine}",
note = "Funding Information: The authors would like to acknowledge the support provided by the deanship of scientific research at King Fahd University of Petroleum & Minerals for funding this work through project No. IN171032. Funding Information: Received by the editors July 4, 2018, and, in revised form, March 28, 2019. 2010 Mathematics Subject Classification. Primary 47H09; Secondary 46B20, 47H10. Key words and phrases. Br{\o}nsted partial order, Caristi, Ekeland variational principle, fixed point, weighted graph. The authors would like to acknowledge the support provided by the deanship of scientific research at King Fahd University of Petroleum & Minerals for funding this work through project No. IN171032. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",
year = "2019",
doi = "10.1090/proc/14642",
language = "British English",
volume = "147",
pages = "5313--5321",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "12",
}