@article{b043cbbc564540d0bc5c67ede22d4f2f,
title = "GRAPHICAL EKELAND{\textquoteright}S PRINCIPLE FOR EQUILIBRIUM PROBLEMS",
abstract = "In this paper, we give a graphical version of the Ekeland{\textquoteright}s variational principle (EVP) for equilibrium problems on weighted graphs. This version generalizes and includes other equilibrium types of EVP such as optimization, saddle point, fixed point and variational inequality ones. We also weaken the conditions on the class of bifunctions for which the variational principle holds by replacing the strong triangle inequality property by a below approximation of the bifunctions.",
keywords = "Ekeland variational principle, equilibrium problem, fixed point, weighted graph",
author = "Alfuraidan, {Monther Rashed} and Khamsi, {Mohamed Amine}",
note = "Funding Information: Received by the editors September 14, 2021, and, in revised form, November 6, 2021. 2020 Mathematics Subject Classification. Primary 49J40, 47H10; Secondary 54E50. Key words and phrases. Ekeland variational principle, fixed point, equilibrium problem, weighted graph. The authors were funded by the deanship of scientific research at King Fahd University of Petroleum & Minerals for this work through project No. IN171032. Publisher Copyright: {\textcopyright} 2022 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0).",
year = "2022",
doi = "10.1090/bproc/117",
language = "British English",
volume = "9",
pages = "33--40",
journal = "Proceedings of the American Mathematical Society, Series B",
issn = "2330-1511",
publisher = "American Mathematical Society",
}