On the Solvability of Generalized Set-Valued Equilibrium Problems


  • P. Chaipunya King Mongkut's University of Technology Thonburi (KMUTT)
  • P. Kumam King Mongkut's University of Technology Thonburi (KMUTT)


In this present article, we consider the generalized equilibria accompanied with certain multi-objective multifunctions. This class unifies numbers of problems surfaced in the area of optimization including the well-known mixed equilibrium problems. Some theorems are adopted, under the conventional assumptions of continuity, convexity, and coercivity on the objective functions, guaranteeing that these functions enjoy the existence of such equilibria. The consequences of this generalized class are of course studied and presented as well.

Author Biography

P. Kumam, King Mongkut's University of Technology Thonburi (KMUTT)

Poom Kumam was born in 1978 in Chantaburi, Thailand. He received his B.S. degree in mathematics education from the Burapha University, Chonburi, Thailand, in 2000, M.S. degree (mathematics) from the Chiang Mai University, Thailand, in 2002, under the supervision of Professor Sompong Dhompongsa, and Ph.D. degree (mathematics) from the Naresuan University in 2007 under the supervision of Professor Somyot Plubtieng. His thesis title was "On random approximation and random fixed point theorems". He started his occupation as a Lecturer at the Department of Mathematics, King Mongkut's University of Technology Thonburi (KMUTT) in 2002. In 2008,?? he received the grant from Franco-Thai Cooperation for short-term research at Laboratoire de Mathc'matiques, Universitc' de Bretagne Occidentale, France. Furthermore, in 2011, he had an opportunity to take a role as visiting professor at Kyungnum University and Gyeongsang National University, The Republic of Korea. In 2012, he take the same role, visiting professor, at University of Alberta, Canada. Especially, he won two most important awards for mathematicians. The first one is TRF-CHE-Scopus Young Researcher Award 2010 which is the award given by the corporation from three organizations, TRF (Thailand Research Fund), CHE (The Commission of Higher Education) and Scopus (Elsevier Publisher). The second, in 2012, he received TWAS Prize for Young Scientist in Thailand which given by The Academy of Sciences for the Developing World TWAS (UNESCO) together with the National Research Council of Thailand.

Now, he has got an academic position as an Assistant Professor since 2007. His research interests include fixed-point theory in both pure science and applied science. He serves the research community as a Managing Editor of the Thai Journal of Mathematics and the Assistant Editor of the Journal of Nonlinear Analysis and Optimization: Theory & Applications. Kumam has started his research in the area of nonlinear analysis since 2000. His research targeted fixed-point theory, variational analysis, random operator theory, optimization theory, and approximation theory. He has provided and developed many mathematical tools in his fields productively over the past years. His results have a wide range of applications not only in mathematics itself but also in physical science, chemical science, biology, statistics, economics, computer science, and engineering. The total citation of Kumam counts 166 times by 66 scholars in the MR citation database (AMS) and 162 nonself citation in Scopus over his 225 publications during 2004 and 2012.





How to Cite

Chaipunya, P., & Kumam, P. (2018). On the Solvability of Generalized Set-Valued Equilibrium Problems. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 9(1), 13-24. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/303



Research Article

Most read articles by the same author(s)