Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Ekeland variational principle on weighted graphs


Authors: Monther Rashed Alfuraidan and Mohamed Amine Khamsi
Journal: Proc. Amer. Math. Soc. 147 (2019), 5313-5321
MSC (2010): Primary 47H09; Secondary 46B20, 47H10
DOI: https://doi.org/10.1090/proc/14642
Published electronically: June 14, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47H09, 46B20, 47H10

Retrieve articles in all journals with MSC (2010): 47H09, 46B20, 47H10


Additional Information

Monther Rashed Alfuraidan
Affiliation: Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Email: monther@kfupm.edu.sa

Mohamed Amine Khamsi
Affiliation: Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968
Email: mohamed@utep.edu

DOI: https://doi.org/10.1090/proc/14642
Keywords: Br{\o}nsted partial order, Caristi, Ekeland variational principle, fixed point, weighted graph
Received by editor(s): July 4, 2018
Received by editor(s) in revised form: March 28, 2019
Published electronically: June 14, 2019
Additional Notes: 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.
Dedicated: Dedicated to Asbaikha and its people
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society